Got a great answer from someone who perhaps preferred to be anonymous:

There is no problem coiling up excess coax. As long as you don't coil it too
tight. There is a 6" minimum bend radius for RG-8 size cable. The inductance
thing is something someone got garbled. Coiling it up will create inductance
for signals flowing on the outside of the coax. This is called a choke balun
and is commonly used at the feed point of the antenna. It has no effect,
other than the length of the cable adds a little loss, to the desired signal
that is flowing on the inside of the cable. Remember in coax the desired
signal flows between the inside of the shield braid and center conductor.
Any signal flowing on the outside of the coax has no use and may be
undesirable. This is why you can tape coax to masts and bury it underground
with no effect on the signal. On 80m there is not always a reason to cut the
cable just long enough to reach, but on VHF/UHF excess length just means
more loss in the coax and is not desirable. Also if you have a lot of extra
coax coiled up and you are using a tuner to say make the 80m dipole work on
30m the extra length could cost you something. For example I use my
160/80/40/30 dipole array on 60m (5MHz) band. The Z of the antenna is
something like 388-j1200ohms. This high SWR increases the loss in my coax by
allot on 60m. In fact the loss is 7.5db. This means my 100 watt is reduced
to 18 watts at the antenna. If my feed line was shorter the loss would be
less of course. So in this case if I had a lot of extra feed line, short[en!]ing
it could really improve my signal strength.