And what about spacesuits? I wonder why they are so uncommon in the 23-24 senturies, and if radiation/decompression/biohazard/life support failure SUDDENLY appears, people just keep asking transporter engineer if he has already locked on the away team. But when you are, for example, beaming on the 100 years old ship drifting in space, or some damaged vessels, you would probably want to be protected from some immediate threat - to take a spacesuit with you, giving transporter engineer time to save all the redshirts' atoms or even don't mind the vacuum/radiation and just continue exploring/investigating. After all, 200-300 years is quiet enough to make spacesuits more comfortable and protective (even cool-looking as we are talking about the TV show) than those that we have now. Because colored shirts are really bad protection from radiation exposure, Spock guarantees that. Also, they could record mission on personal badge cameras or something (maybe they do, but not always - TNG "Identity Crisis") and transmit image on the bridge main screen instead of reporting by communicators. But Yes, it wouldn't be the Star Trek that we know. It never tried to look realistic. The ENT series were closer to our 21 century reality and that show was completely different from the TOS or TNG.
That's not really true. The producers--at least on TOS--expended considerable effort trying to keep the show plausible. Roddenberry reportedly consulted numerous experts (not to mention keeping deForest Research practically on retainer) on various futuristic aspects of the show. (Consultations that, IIRC, led to changing "lasers" to "phasers," for example.) What they didn't do was lose track of the fact that they were making dramatic entertainment, not a documentary.
Enterprise was no more "realistic" than any of the other series. Though I am curious: how are those helmsmen, navigators and other dedicated personnel suppose to gain experience to advance their careers if they're always chained to their duty stations and not allowed to carry out other types of duties? Exactly.
In reality you might have one officer with a number of enlisted people. The officer would probably be an engineer/scientist as the mission requires, you'd have a security guard, a medic, some lab assistants or engineers as the mission requires. You definitely wouldn't ever see the captain, nonetheless half of the ships command structure. But of course one person we might know and a bunch of no-names doesn't make for good television.
Oh yes they would have environmental suits for sure. I loved ENT's look and style. To me Trek,TOS and TNG filtered though the time they were filmed. TOS screams 1960's future, the colors, the outfits and the bad FX, which may have been fine in its time. TNG does the same thing, its filtered though the idea of what trek would look like from 1990's point of view. ENT does the same thing, it shows us what we think it would look like form a more modern view and it had better FX and better effects because the technology was there to do so. To me it has the best "look" of all the treks. I would love to have seen a whole relaunch of TOS era with that look and feel. I mean..just look at this sweet, sweet ride