The DM has to do that also, but with more characters, significantly more, they might not need the same depth, but they definitely are keeping track of more character's abilities, and they have a lot less time to "get into" the role as it were. Your players could be like "Hey let's go to this Tavern" and suddenly you're either playing a character you haven't played in months or inventing one whole cloth.
The DM also has to recall all of his stupid plot points, NPCs and clues, and has to remember ones the players don't know about if he wants to foreshadow things properly. And I have to decipher my notes to, if my players think what I tell them is confusing they should look at my notes.
Yep, and if your group is active enough you can sometimes take a back-seat there too.
All of this is true generally. With the exception that it's not "knowing" the rules that stops you getting bulldozed, it's not letting people bulldoze you.
Except you don't. Unless you're running a complete sandbox which is really challenging (imagine having to keep track of half a dozen MORE moving parts than normal. I don't get to react to the players, because if the players say "Hey let's go over here" I need to have something ready for that. Now you can be like "Hey I didn't realize you guys would go here, can I take fifteen to figure this out" but that's clearly you not knowing something.
Also you'd better have an idea of how your players are going to solve problems because if you don't they will not be able to solve them.
DMing is more challenging, but also more rewarding. As a player, I'm not making it so that five to six people who might not have been able to play D&D (or whatever system) can. As a DM I get to do that, and that's amazing. I get to build a whole world, and even if it sucks, players will enjoy it. I actually had to get really retrospective and start doing serious self-evaluation when I realized that players will tell your game is good, even if it's not, and you have to evaluate yourself.
I also like playing, because you can really inhabit a character while doing that. I miss playing a lot, since I don't get to do it often.