exactly, and there's even something before - the musician. a vocalist or a sax-player with a good microphone technique (yes, this is not very common) don't need any further dynamics (comps, gates) or spectral (EQs, filter) processing. a good vocalist will be very carefull with "ssss" or "pops" and maintain a consistant level no matter if they are whispering or singing a hard-rock chorus. listen to real studio musicians if you don't believe it. the best recordings where made in that way.
but there are still occasion where processing is always needed. drums for example always sound bad after recording, except if you like trashy drum-sounds. drums need many tweaks to sound right.
it is always a good way to use a minimalistic approach processing your signals. and explain your recording problems (like sss or loudness, clipping) to the musicians and you will hear a noticable difference after some practice. this is better & cheaper than any processing.