James Bond and Batman are iconic pop culture characters that are larger than the actors that play them, while Don Adams IS Maxwell Smart, Don Johnson IS Sonny Crockett. So the question is - are the characters of Kirk and Spock like Bond and Batman, or are they more like Crocket and Maxwell Smart?
Honestly, if you're going to compare apples to apples, then Kirk and Spock are like Crockett and Maxwell Smart.
Bond is a literary character who was created and physically described by a particular author. The actors simply portrayed a pre-existing character, same with Batman. He's been played by different actors from day one, like Tarzan and Sherlock Holmes. People will accept them based on whether or not the actor "makes a good Bond" or "is a great Batman." These actors are playing characters pre-made and work to fit the personalities.
Kirk and Spock (and therefore Crockett & Smart) were created by the actors. The characters, because of the hectic schedules of filming, wound up basing much of the personalities on the actors. James Kirk WAS William Shatner, because he brought everything we saw to the role. Sure, he was created on the page by writers, but by the time we saw the finished product, it was delivered and represented by the actor. It is a much stronger image, because a literary character is formed in the pages of the book but also in the mind of the reader. Different readers will conjure up different images. However, Shatner was ON TV. We saw exactly what he looked like, what he sounded like, how he walked, talked, laughed, ran, etc. No imagination was needed on our part. In order to be true to the character, the actor would have to be playing a young Bill Shatner. Shatner wasn't "version of" the character, he was the actual character.
Instead of comparing Kirk (or whomever) to other literary characters, you should compare Shatner to an AUTHOR who creates the character. Do you like Bond novels written by the authors after Ian Fleming? Does Bond sound the same? Is his character in line with Fleming's version or is it different? And do you like those differences or not? It's up to the individual.
Nobody but the original actors will bring all of the things we loved to the characters. That's fact, because every actor is different and the actors created the characters. Chris Pine might make a "good Kirk", but he will never be the Kirk we knew. He will be "New Kirk" or "Chris Pine's Kirk."
Other people can play the characters, but they are not in the same category as the Bond or other literary / print characters. Over the decades, at least seven people have played Superman in live action productions. There have been three David/Bruce Banners, eight Batmen and so on. But in all of the years from 1966 until 2009 there has only been one James Kirk, one Spock, and so on (I do not count the New Voyages fan flicks - sorry).
They new actors can be accepted, absolutely. But whether or not the Star Trek characters should be considered timeless classic creations to be reinterpereted over the decades is something else.