You know whenever I hear someone describe TOS as "the ship and crew were completely on their own without a Starfleet Command to call for backup" I honestly have to wonder if that person or persons has ever watched TOS, because that was not really the case.
In fact they frequently running into other Starfleet vessels and stations. And if they weren't doing that they were visiting federation member planets and colonies, or had dealings with federation officials.
Frequently, yes, but not constantly. There were other episodes that were predicated on the ship being isolated, having to wait weeks even for a response from Starfleet Command, so that Kirk had to be the one making decisions that could make the difference between war and peace. "Balance of Terror" is a prime example. The point isn't that TOS was always like that -- the point is that it could be
like that, could tell that kind of story in a way that TNG rarely could.
Absolutely. Also the TOS crew didn't have 'direct' communication with Starfleet command, and on several occasions part of the drama is that it could take days for Kirk's communiques to get to them and a further few days for a response to make its way back to the Enterprise, in which time Kirk still needs to deal with the problem at hand. So there was a degree of isolation there, where the crew had more autonomy than TNG (where communication with Starfleet was often only a case of opening a direct channel). I think Voyager was a deliberate attempt to go back to this template, to make it so the crew had to solve problems for themselves rather than ask for advice and follow orders.
A show about a ship being is more isolated doesn't necessarily make it better.
TNG wasn't trying to be TOS. They were set during two different eras of the Federation.
In TOS, space was still quite unexplored and they were alone very often.
In TNG, the Federation has grown in considerable size and it had become more about keeping the peace. The tensions between the Federation and the Klingon Empire had lessen after they had become allies. That alliance pretty much kept the Romulans in check. The Federation was enjoying a period of harmony that it had not known for decades.
There were of course exceptions, like the two Borg incursions into Federation territory, and dealing with the aftermath of the first Cardassian war.