Probably, but it is fallout from other equally arbitrary decision. The
first question you need to ask is how good do you want the voice
quality, or how fast do you want the basic data rate to be. Depending
upon the modulation scheme you want to use, determines the required
link margins.  Generally local regulations set a limit on the energy
you can emit from the hand held phone.

Given those assumptions, you can calculate the capacity for each 1Khz
of spectrum you want to use. You then decide how much capacity you
want in each 'channel' (it's actual bandwidth), and everything else
will sort of fall out.

The underlying data rate in the phone  is about 14,400 bits per
second.  you have a 200kHz wide channel, and unless you want to get
really fancy, that places the channel capacity at sometihng around
200K -400k bits/second.  to the  guard band (time between adjacent
time slots)  from the design, how much you need to 'package' the
payload and for supervisory information. Add it to the basic data link
rate, and back out the lost capacity in the channel due to guard band.
Ultimately have the useful capacity of the channel, divide it by what
each call or equivalent data service needs, and out pops the number of
ways to divide the channel.

The point is while there may indeed be a mathematical reason for 8 (or
16 if you run HFR), it can all be shown to result from  arbirtary
decisions made further up the decision tree, so in the final analysis,
the 8 slots results from an arbitrary decision.

D-AMPS uses 3 slots,and it is pretty easy to work out how that
happened. You look at the requirement, the main one is that has to be
able to coexist with AMPS, so you have a 30 Khz channel to work with.
D-AMPS uses a more sophisticated modulations scheme, and a lower
payload datarate (about half of the GSM rate). As a result, D-AMP put
about twice as many channels into the same piece of spectrum that GSM
does. The D-AMPS capacity was a direct consequence of the need to fit
within an AMPS 30Khz channel, and to try to maximize the capacity of
that channel, even if it meant the loss of some voice quality, and
difficulties in adding features.