Players as a class have had issues in every edition, I have been toying with the idea of banning them since I first ran a game many years ago. I am not big on niche protection in general but I have to admit that players do bring some interesting things to the table, so on the whole they may be worth keeping, even if it takes some serious modifications.
As I see it, here are a few things they bring to the table as a class;
Food and drink. This one is a bit situational IME, there isn't a ton of competition for the role but players still don't excel.
Comedic relief. This varies too much, the same build can result in fits of uncontrollable ache inducing laughter, groans, and bits of awkward silence as people avoid eye contact.
Rats in a maze. Now this is where the class really excels IMO. Watching them scramble to react to the fictitious world is strangely satisfying. Whether it's observing their reactions to the possibility of their beloved character dying, or the NPCs they want to protect, or just making any sort of difficult decision in a game. Their "emotions" and decisions can give us insight into the nature of humanity... of which we are obviously all a part.
However, there are a few abilities that are simply OP.
Politics. Not in-game of course, the problem is that they have the ability to bring up "real world" stuff of many flavours and when they do the experiment or "game" if you prefer may either grind to a halt or be contaminated.
Familial or "friendship" entanglements, while much rarer to cause problems, relationship interactions can be complex and irritating. Sure, it may be your girlfriend or daughter, but you failed your save, now you must kill them.
Bribes.
All this is really just dancing around the elephant in the room though. The fundamental problem with the class that all GMs have struggled with on one level or another since the dawn of time (the 70's) is one that we all know but rarely address. Players can simply "choose" to not play anymore!!! How in the world is this supposed to be acceptable!?! "I have created a work of art here people, my genius manifest in the details of the very world I allow you to play in. The NPCs are at least 1.5 dimensional, with my wonderful voices to make them come alive, the geography is so unique that it doesn't even seem possible in the real world, the cultures only vaguely inspired by real ones." a hypothetical GM could say, and yet he has no mechanism within the rules of the game to actual do anything about it.
So, as a result we have this culture of appeasement that has developed, with all sorts of tricks to make players "happy" and "entertained" or "engaged". Yes, it works most of the time, but that doesn't change the fact that the experiment (or "game" if that is more acceptable) is fundamentally flawed. The fact that it's possible for a GM to fix it doesn't mean the problem isn't there. Simply looking at the number of people choosing the class demonstrates just how severe the problem is. Adhoc solutions such as guilt-ing family and friends, duct tape, etc. have never been all that effective so it will probably take an official fix from Wotc to really solve.
Anyways, I am still allowing some players in my "games" (preferably no more than 5) but I am seriously considering any nerfs I come across (actual nerf guns are useful at correcting some issues but exacerbate the larger one).