They'd have to solve the "transporters damage your reproductive system" problem (from A Choice of Futures) first. However, given that we know they did solve this problem eventually that's not a big issue.
That's not the case. Rather, early transporters could cause cumulative minor damage with heavy use, and this could potentially manifest as various different forms of systemic damage depending on the individual and on the luck of the draw. Malcolm Reed suffered reproductive damage, Jonathan Archer suffered loss of motor functions, and Trip Tucker, the other heaviest transporter user, suffered no evident long-term damage.
As for the age thing, McCoy was 137 in "Farpoint" and modern Trek has made a habit of retconning all the once-unique 24th century abilities of Trek into the 22nd and 23rd. So Archer living to a ripe old age really isn't that much of a big deal.
And yet Mark Jameson in "Too Short a Season" was ancient and feeble in his 80s. And let's not even talk about "The Deadly Years."
Also, you're confusing "possible" with "routine." McCoy living to 137, as I said, was portrayed as exceptional, an accomplishment in its own right. In DS9, Jadzia once told O'Brien she expected him to live to 140, but in terms that indicated she saw it as a ripe old age, near the maximum possible for humans. Statistically speaking, nearly all humans would live shorter lives.
Especially someone like Archer, an early space explorer who was exposed to all sorts of unprecedented dangers in space, dangers that humanity wouldn't yet have discovered ways to protect against. Even aside from the transporter thing, there's no telling what kinds of exotic radiations he was exposed to, what kind of long-term damage he and his crew suffered from exposure to the spatial distortions in the Expanse, etc. Fans want their heroes to live forever, but the harsh reality is that NX-01's crew would be far more likely to die young compared to the average.
And yes, reality matters, at least to me. To my generation,
Star Trek was the most plausible, realistic, and well-researched science fiction show on television by a huge margin (or rather, the only one that even tried to be plausible). That believability was a key element of its popularity, because it made the show feel more real and important to us, made us willing to buy into its reality in a way we couldn't do with more lowbrow, fanciful shows. It's frustrating to have that view of
Star Trek and see everyone else these days treating it as pure fantasy that doesn't have to make any sense.
Because peoples beliefs don't generally stem from rational facts, they come from feelings and what they prefer to be true. See: Trump, Brexit, etc.
Which is something that should be challenged and questioned, not shrugged off and settled for. If more people learned to think critically, those things wouldn't have happened.
