No, that's taking the analogy far too literally.
It's obvious that you and Temis wanted a middle ground, but Temis wanted the same actors returning to play different roles. This as a practice makes more sense for an anthology series where stories are not supposed to have 'happened' in the same universe, though it is of course something you also get in non-anthology TV (and there are countless examples from Star Trek alone.)
I was drawing a line between the model of anthology TV - like the Twilight Zone and the Outer Limits, shows which do not need internal continuity of any kind - and episodic TV, which is what most Star Treks have been about. Episodic TV like anthology TV has the ability to be about a different story each week, and even be about entirely new characters each week, but it also has an established cast of characters who work through the premise of the week's story and indeed can be a focus for the story itself.
I think a series that treats seasons as independent stories but has that level of character continuity would feel more like Star Trek and further take advantage of the continuous universe aspect to actually have characters we'd recognize regularly showing up, which is kind of a big deal for TV shows.
Yes, there are certain expectations, but those expectations should be challenged, because that's what distinguishes good, fresh, compelling storytelling from safe, conventional, uninspired storytelling.
True but my point is less 'what is a better story' and more 'what can TV sell a broad audience on.' Instead of looking at Star Trek as a universe with numerous species and factions and centuries of history, Abrams approached Star Trek as a media property with iconic elements that are well known parts of pop culture: Kirk, Spock, the Enterprise, the guy who wears red and dies horribly.
Deep Space Nine was probably the one series that invested itself the most in letting its involvement with the mythos try to cancel out its relatively unusual premise. It began without a starship or a captain and with the majority of the cast being aliens, some of which were aliens already very familiar from TNG, and dealing with the political fallout of a planetary situation that had been referred to a couple of times on that program and featuring in a key role one of TNG's lower rung antagonist races.
It also - like Voyager, a decidedly safer show - had steadily declining ratings.
But that's not the only possibility. If Starfleet can put together a crew with diverse talents and send them out into space, why can't, say, a civilian research institution or university do the same? Why not go with the Trek-universe equivalent of Jacques Cousteau's Calypso, say?
But can't we have both? This is where the underexplored idea of Starfleet having large civilian components to their crew could be relevant. You could have a starship with university faculty and/or experts in various fields in addition to
Starfleet personnel. It could be a ship where the scientists basically decide the itinerary and examining spatial phenomena and strange new worlds (say starship mills in orbit as anthropologists study social behaviour of pre-industrial sea beings and archaeologists extrapolate existence of a once more advanced civilization that perished with an unclear catastrophe) but the starfleet crew take charge in case of a crisis (sea beings want to sacrifice anthropologist and they can't transport because of... whatever interference in the water).
I mean - being Star Trek - these people are no doubt going to encounter situations that put them in physical danger. So you either have them include people who are sufficiently skilled at extricating them from that danger but who are not Starfleet for whatever reason, or you have people who are Starfleet.
In other words it's a series about people doing the things we associate with Starfleet without being Starfleet. Hence:
As I already said, that would be tantamount to watching JAG and NCIS and assuming that all criminal investigation in the United States was done by the military.
I think it'd be fair to say that all things pertaining to the military in the United States are done by the military. And Starfleet has treated as both space and ground forces, though the lore about the existence (or non-existence) of Starfleet marines has always been a bit fuzzy.
Who starts shooting when things go south, is kind of the question there. University students with phaser training? Civilian starship crew who have done this kind of crisis management before? Etc.