Why is this question important? Or, more specifically, why is it important and to whom is it important?
It is important because pistol manipulations should be founded on a well thought-through basic pistol concept.
For every shooter, the basic education is the foundation of any performance with the pistol, for an armed professional, a legally carrying citizen and a sports shooter alike. The underlying pistol concept for all of those types of shooters is the same, including the basic manipulations such as magazine change and emergency reload. The principles of efficient and effective pistol craft do not really differ, even if the purpose and equipment do. Of course, the actual implementation and also any advanced, specialized pistol education can differ quite a lot. Nevertheless, the question about dropping or not dropping magazines is important to all shooters.
Let's take the example of sports shooting. If you are competing in IDPA, you will know about dropping or not dropping magazines. There are numerous rules about when and how one is supposed to reload and under what circumstances one might get penalized for dropping the old mag to the ground or not.
In certain cases, there's an obligation to retain the old magazine. Retaining means keeping the old magazine with the shooter after the change. Why would one want to do that?
Here's some background:
Retaining the magazines with the shooter comes from a military firearms education background. If you have done some kind of military service, you might have noticed at some point, that military organizations are not fond of their soldiers loosing equipment. Any kind of equipment. That's true for the spoon you use for eating your meals up to more obvious stuff such as ammunition or your personal weapons. Especially your personal weapons. After all, what's the use of a soldier without his weapons? That should be fairly easy to understand, right?
Now, next point: a magazine is quite an important part of the personal weapon. Without a magazine, your wonderful, high-capacity, high-firepower personal weapon is degraded to an inefficient and super slow single-shot piece of s**t. Not good.
You will get issued a number of magazines but if you keep dropping and loosing them all over the place during any engagement lasting more than a few minutes, you will run out of usable magazines fairly quickly.
It's neither practical for the army to somehow provide you with an endless supply of brand-new magazines, nor will they enlist some special detail of servants picking up behind you and carrying your mags around so that they don't get lost.
Furthermore, if those mags you keep scattering around the countryside still contain any number of rounds, it's even worse to leave them lying around. Firstly, the enemy might use that ammo against you and secondly your gun is further downgraded to a glorified stick without ammo. Of course, the army will have to provide you with some supply of ammo once in a while, but the purpose is to use that against the enemy and not to seed the dirt with it.
Hence, a good military firearms education includes retaining the mags and the rounds, whenever possible. In that way, soldiers are better able to stay effective over any longer period of time. Got that point as well, I hope.
Police and Civilian Self Defense Perspective
So, that aspect of military firearms education should be clear. But what about police, armed security or civilian self defense, or - in general - civilian firearms education? There are no long operations in the battlefield, no re-supply challenges and so on, right? Is there still a point in retaining magazines?
Whatever the confrontation scenario might be here, I am not going to get lost in endless debates over what if this or what if that. Just one thing: if you have your mags with you, you can use them again later. If you haven't, you can't. That should be undisputed for all novices and experts on this topic alike. Now make your own decision.
How about the sports shooter? Why should you bother with retaining mags? My answer: if you don't drop them, they can neither get damaged nor do they get dirty. Ever had a malfunction because of a bent or broken magazine lip or dirt blocking the follower? I have. I have even seen mags disassembling themselves when hitting the ground. The base plate flew right off and the spring, follower and the rest of the ammo where all over the floor. I didn't find that to be ideal. Those where 1911 mags however, and maybe they need special 1911-type treatment or tuning. Haha just teasing the 1911 die-hards here. Anyway, that's another topic.
Back to a sound pistol concept, in particular to the manipulations 'magazine change' and 'emergency reload'. While their execution is similar, their context and their activation triggers are very different.
The magazine change is performed when there is no immediate need for the shooter to engage a target. The gun has been fired and is still capable to continue firing but the shooter decides that he wants a fully loaded gun at his or her disposal. The decision is to establish optimal conditions, as far as the gun is concerned, for whatever might come next. It's a conscious choice and circumstances allow for the manipulation. Therefore, there's no problem with retaining the mag for potential further use later on.
The reload however, is performed in a desperate emergency situation: there is an immediate need to continue engaging targets but the pistol has run dry and is not capable to fire. The shooter has no other choice but to reload immediately. The absolute priority is to continue shooting and the shooter should make no non-contributing efforts besides getting the gun ready to fire again. That includes fumbling with the old mag, trying to retain it somehow.
This reload is properly called emergency reload and falls in the same category as the malfunction drills: you have to shoot immediately, but you can't. A catastrophe. Something to be avoided whenever possible in the first place.
Why do sports shooters like to drop their mags? What many people do is a actually a mag change but with dropping the old mag instead of retaining it. Something like a 'Speed Mag Change'.
Supposedly, dropping the mag is faster than retaining it. And it is. Somewhat. This is due to the fact, that the support hand can immediately go to fetch a fresh mag and does not have to first grab and store the old one. However, the time difference between dropping and retaining usually amounts to less than 0.5 seconds. In my case it is a couple of tenths of seconds. Of course, I practice this extensively and my equipment is prepared for it. Yeah well, you have to practice this stuff of course. If you don't, then talking about gaining some tenths of seconds in speed here, while actually wasting seconds left and right, is a waste of breath.
How do we measure the time used for the manipulations? One simple method is to stand at a fixed distance from the target, say for example 10 m, and then perform a shoot one, mag change or reload, shoot one drill. The split time between the two shots is the time used for the manipulation. Do it at least 10 times and take the average to get a more or less representative value. Then repeat the next day or the next training session. Of course, all of that is only valid if there are two nice hits on target, alphas or zeros. Remember, everybody can shoot fast, but it's the fast hits that we are after. If you measure times without hits you are just cheating yourself.
What? Something for free?
What one should try to do in sports shooting is to manipulate while moving. If ever possible, pair a mag change with some movement you have to do anyway. In this way, the manipulation becomes 'for free' as far as time is concerned. If that's the case, the couple of tenths of a second difference when retaining or dropping the mag become negligible.
If ever possible, try to avoid standing manipulations. However super fast you are in your mag-dropping-reload, you will never be faster than nothing. Only Lucky Luke was faster than his shadow, after all.
Drop or don't drop the magazine? In a concept-based, practical shooting education the magazine should be retained unless there's an emergency situation such as facing targets with an empty or a malfunctioning gun. The magazine change and the emergency reload are taught as different manipulations that are triggered by different circumstances. By the way: how many rounds remain in a dropped magazine is not really a relevant criteria.