twice this century, but I'm going to have to respectfully disagree with Mr. Bit...
There are some "magic" filters out there - might be the cut-off frequency, might be the topology, might be the parts used, I have not yet figured that part out yet, but there are filters that I use because they are just musical. Oddly enough, most are fixed frequency filters - for all the other reasons you listed, but cost is probably the predominant reason.
Examples - the classic Pulteq filters seem really well placed, now do we like them because they are in the right spot or are they in the right spot because we've become accustomed to them?
One of my favorites, strange though it may be, was a cooperative effort between Haffler and Rane - this funky little 1 RU guitar preamplifier that had the most musically useful (for a guitar) tone controls. They didn't even call them filters<G>!
Another favorite was the tone controls on this old Heathkit preamplifier. The filters are all passive, but they just work musically.
Symetrix used to make a couple filter sets that were really useful, and the Urei "Little Dipper" is another one from that era that I really liked.
For modern gear I don't think you can beat the MAAG EQ, that thing is just magic!
Anyway, choice of cutoff frequency is very important, and highly subjective<G>!
Bill