Are there any reasons to remove or not tremolo arm when transporting guitar in a gigbag?
Some Strat. guitars have a small spring which is there to put tension on the bar itself - which is often quite loose in the thread. O.k., some players like it to swing down, but the point is that when the bar itself is unscrewed, there is a liklihood of the spring being lost. One Strat player I work with unscrews the bar, and screws in a small bolt with the same thread design.
The other issue, in my eyes, is that the material itself is quite soft, and constant screwing and unscrewing makes an often already floppy bar even worse.
It also depends on the sort of case.You say 'gigbag' - which I stopped using about 50 yrs ago when it fell over with a guitar inside, and the head snapped off. Not a lot of protection, apart from rain! Gigbags are often flimsy, and the material can catch or be caught by protrusions like whammy bars, so probably best without.
I would take it off. I don't think it'll do much harm to your guitar if you leave it on, but your guitar is likely to be more out of tune when you get it out of the case. (Floating bridges are always more temperamental tuning-wise anyway. That's why I love my Telecasters; once the strings have settled they seem to require very little tuning - great if you turn up late for a gig!)
If you leave it attached, you are likely to catch the tremolo arm on the inside of the gig-bag when putting it in and taking it out, which could cause damage if done with any force.
Also, a small thing: you are more likely to damage your gig-bag if you leave the tremolo arm on. It's fairly smooth, so wouldn't damage it quickly, but all constant use makes a difference eventually.