And statistically you're both right. On average TOS is cut a second faster
per season than TNG and DS9. I haven't enough TV series comparison data to check if TOS is particularily fast for its time or TNG and DS9 slow, but both series rarely resort to the rapid cutting from actor to actor TOS used.
About the datedness ... ANY
artistic product is dated by the time specific influences, just wait a few decades and then look back at the current production. It's just that most people are so completely caught up in the predominant current aesthetic that they find diverging styles odd and dated or campy. Basically there's no reason to prefer one mode of expression to another, slower or faster speed, expressive or minimal acting, lots of camera movement and variation or very little of it, all of them have their legitimation. Contrary to popular perception film language hasn't changed that much since the mid20s.
Generally TOS benefits from some clever stories and ideas, some may be blunt but that's quite fine in the Jonathan Swift tradition. There's mostly an excellent pacing and the series has an excellent dynamic lead actor in William Shatner who manages to make a rather conventional character believable and multi-dimensional. The direction ranges from average to inspired, the effects partly could have been better which is mostly due to the too low budget.
Nevertheless I don't see any need to find excuses for the series on most artistic grounds. It's however unfortunate that there were somy trashy episodes which merge a sexist attitude towards women, silly TV action fistfight plotting and similar vices.