historically, you needed to remove them from Fabers on the regular because they had a really bad boot design that didn't drain so the bottoms would rust REALLY fast. They have since fixed that.
You also wanted to remove them from sets of 8" doubles in particular because the gap between the boots was small enough, especially with the octagonal "standard" tank boots, that line could legitimately get stuck between those tanks causing some exciting gymnastics to be required to get it out, or at least getting quite familiar with your buddy :-D
If you are doing true sidemount squeezy stuff, then you may want to remove them because the lips of the boots can get caught on stuff. It's not normally a big deal, but a lot of people remove them because it's less of a hassle in those situations.
Most people just echo information that they've heard and want to be part of the "cool" crowd so they are adamant against tank boots. I think it's ridiculous, but that's just me.
Now, if you have modern boots, and are diving sidemount, there really isn't a need to remove them unless you really want to. I have them on my HP120 doubles, my LP50's in my CCR rack, and any steel bottles that are set to be used as backmount singles *none at the moment, but have a stack of boots for them*. I don't dive boots on my sidemount tanks, but I also use them for sidemount restrictions in caves. If I was doing anything off of a boat, they would probably have them and many boats require tank boots to not destroy their decks.
If you're diving salt, I'd try to take them off pretty regularly *once a month ish* to clean them, but if you're diving fresh I wouldn't bother outside of vip