I've been trying to play classical pieces recently and I found it easier to play the very fast parts of a song (take fur elise's 2nd movement and the second part of the third movement) by resting P on the lower strings while my fingers IM pick. Does good players do this? I'm not very knowledgeable about classical guitar technique, unfortunately.
I would not recommend placing your thumb on the bass string when playing fast runs on the upper strings. This will only lead to handicap down the road. The fact is that your thumb does not have to go somewhere when not in use. I don't understand the rational behind that statement. You thumb is always attached to your hand so it has a place to go.
You asked us whether or not the good players do this but you don't state who you think a good player is or any criterion for being good. That makes it an opinion based question. Some might say that by definition if a player has a handicap like anchoring the thumb on the strings then they are not a good player. Based on my experience many Flamenco players will anchor the thumb but just as many float it, keeping the distance between the thumb and (i, m) the same. Thus they shift the thumb back and forth when changing strings in a fast run. Still other will keep the thumb close to the index finger and "rest" i on the thumb when executing a free stroke.
The best players I've ever seen do not rest the Thumb but float it. At the end of the day what matters is whether this is something you need to rely on to play or something that you can choose to do. If it is necessary then I would say you are developing poor technique, or no technique, and using the anchor as a handicap that in time will limit your dexterity.
When playing in a classical style, your thumb has to go somewhere. If it's not actually in use, (not playing low notes at that time), there's nothing wrong with resting it on a string - and the low E is favourite. You've found that it helps your playing: your picking hand needs stability. I often find students struggle with this, as their picking hand is floating, not stable. True, it can be stabilised by freezing the forearm and partially the wrist, but why bother when there's a method that suits better.
Bassists use it frequently, resting the thumb on the lowest string, sometimes moving it across to the next lowest when playing the top string. It also has another advantage. It mutes the string it's on. Thus cutting out extraneous noise from that string.