Kirk was definitely a bit of a swashbuckling character, but I think the womanizer thing is exaggerated:
Per the internet:
In the original Star Trek series, Captain Kirk actually had sexual encounters with very few aliens, with estimates typically ranging from 2 to 4 specifically alien, out of fewer than 10 total romantic liaisons. While the "interstellar womanizer" reputation is exaggerated, key examples include Deela in "Wink of an Eye" and potentially Elaan in "Elaan of Troyius".
BTW - I would have no problem if the Star Fleet Academy Chancellor had a lover or occasionally went to San Francisco or Risa for a hook-up. If Hoshi Sato (ENT) can do it, why not other officers. The issue is professionalism, discipline, and leadership while on duty or when interacting with subordinates. Also, what is the deal with these barefoot close-ups? Does someone in the writers' room have a kink or fetish?
So? How many incidents would you consider to be acceptable for the captain of the flagship on what is a to a large extend a diplomatic mission?
Now it was what TV shows did at that time, but once you take a step back you just can't unsee that TOS was just as cringe as Discovery and now Academy are accused of being.
Obligatory ST Convention, and the definition of the verb "Riker":
In a sense, you could say that Wheaten Rikered the hell out of Ashley Judd.
BL.