There are very few criminals with this level of insanity anymore, so one on-site doctor is enough to treat them all – other medical consultants, if necessary, could be consulted remotely via subspace. Considering how dangerous these criminals are, and how decent folk probably don't want to have such a place in their backyard, I'm not surprised StarFleet would put it someplace that had good conditions (temperature, gravity) but was otherwise was not qualified for colonization (poisonous atmosphere). Most planets are more likely not right for colonization, but they can still be used. Plus it helps keep the prisoners in since they can't escape outside so once past the force field they can beam someplace.
As for the counter sign, the first time Kirk visited such a place, Simon Van Gelder beamed up and Kirk probably is still taking crap for that. So he added an extra level of security and made sure either he or Spock was on hand to personally make sure that kind of thing didn't happen again. Makes sense to me, given his history.
IMO, Spock should have just stunned them both and sorted them out later, but that's me.
I completely get the benefits of isolation and such, but a *poison* planet still seems like serious overkill. And one doctor on his own has to sleep and ought to get some time off sometimes and can easily have an accident, etc. Even if it was just a single patient, I'd still expect at least two staff just on the general buddy principle.
You're right about van Gelder, though, I'd forgotten about that. That makes much more sense now.