People die (anybody else notice no one was killed in the first two seasons or permanently maimed over the entire series?). I submit that's not realistic and detracts from the reality (and drama!!) of space travel.
However, crewmembers suddenly started to die on a regular basis in Season 3. In retrospect that made a lot of sense, because it did underline the dangerousness of their new mission. While they had conducted "harmless" exploration in Seasons 1 and 2, things got rough in Season 3.
Unrealistic is the high number of redshirts who had to bite the dust in TOS. Acccording to "Ex Astris Scientia" (
http://www.ex-astris-scientia.org/tos.htm), the original Enterprise lost approximately 56 crewmembers. So, strictly speaking, they only had a crew of 374 instead of 430 at the end of their 3rd season (unless the NCC-1701 refreshed its stockpile of redshirts at a starbase each week).

But that's why TOS is sometimes fun to watch...
As for the OP's question: Well, the main problem since Voyager was to come up with original ideas. They wanted to create something entirely new with Voyager, but in the end they produced "TNG-lite". They wanted to to go in totally new directions with Enterprise, but they mostly ended up with "Voyager in the 22nd century" instead... at least in their first two seasons. Without the TNG/DS9/VOY "baggage" a lot of the ideas used in Enterprise would still have been new and original, so maybe the show could have been more successful.
However, instead of "erasing" the three 24th century series from existence, I would have preferred that the 4th season of Enterprise had actually been the 1st season of Enterprise. That way, the series would have used its potential from day one: Go with the "Birth of the Federation" concept by showing how mutual cooperation between the founding members of the future Federation came into being, instead of wasting time on a "Temporal Cold War" arc where not even the writing staff seemed to know what the point was. Instead of having the Ferengi, the Borg or bland new alien races like the Suliban show up, concentrate on exploring underdeveloped TOS cultures like the Andorians, Tellarites, or Orions.
In addition, I would have kept the technology a bit more "primitive". The grapplers were a good concept, as were the torpedoes from Seasons 1 and 2. But I would have gotten rid of the Transporter entirely. And I would have never introduced the "photonic torpedoes". They also should have kept the plasma cannons and pistols from "Broken Bow" instead of replacing them with "phase cannons" and "phase pistols". Ah, and the "hull plating" was only a thinly disguised stand-in for shields.
So, to summarize my proposals to improve Enterprise (if I were only an exec at Paramount and had a time machine

):
- No transporter.
- No phase pistols, phase cannons, or photonic torpedoes. Use plasma weapons and the more primitive spatial tropedoes instead.
- Don't treat the hull plating like shields (= no "polarization").
- No Temporal Cold War.
- No Suliban, Xindi, Ferengi, Borg or aliens-of-the-week who could have appeared on Voyager just as well. Main races: Vulcans, Andorians, Tellarites, and Orions. Maybe also some appearances by the Klingons and Romulans, but not too early in the series.
- Use the Season 4 themes from the start... birth of the Federation, prelude to the Romulan War, exploration of the cultures who later founded the Federation, conflicts between those cultures, maybe some Eugenics Wars stuff like in the Augments arc.