Yeah, I defo agree that RTwP is more appealing for people who want to focus more on story and the world, and we look for different kinds of fun in a BG game. On the other hand I feel like TB crowd is more interested in playing aforementioned chess/puzzle style combat. This is also why you will often notice RTwP folks say that TB feels like it's just there to waste/pad playtime.
We want combat as an exciting part of story, and fighting 6 rats for 5 minutes (exaggerating) sounds neither exciting not flowing with the story.
Fighting large crowds of relatively weak enemies is a great way to deliver on power fantasy or story (for example storming a keep, or fighting in a large scale skirmish). And TB sadly pads time like crazy when it comes to large fights. It also makes them feel less chaotic, which is a bad thing considering that often large scale fights are meant to be chaotic. And yes, as all things these should be used in moderation. They can feel great and refreshing in RTwP, while in TB they are almost guaranteed to get annoying fast.
Another problem with TB is that it has too much downtime when you just sit and watch AI do it's turn. Personally, it's second biggest deal breaker for me - I want to be playing, not waiting and watching.
Next big one is that you have to micromanage your entire party at all times. Again, I prefer to play my character and let party do their thing, only micromanaging them when required. I love putting some gear on them, picking some spells for them to use (although I'd rather have a "suggested level up" pop-up that would hopefully save me from screwing up too bad). I like to think of my party as somewhat self sufficient companions that can hold their own if needed and who can make use of what PC gives/suggests them, and PC as the party leader who sometimes tells everyone what to do, but mostly lets them go about it in their own way. This is probably a number one deal breaker for me - having no AI to manage my party while I focus on experiencing my main character. When I sit down to play, let's say, a rogue I want to play a rogue, I don't want to also play cleric, and warlock, and ranger, and fighter. I wouldn't complain if I have to sometimes exercise some direct control, but only for really difficult stuff like bosses.
Another problem is narrative pacing. TB takes a lot more time. For example chasing a bad guy who sends his cronies to cover his escape will feel pretty ok in RTwP, because you can deal even with several waves of them pretty quick. TB will drag it out much longer an will (imo) stop feeling like a chase. TB really screws with the time passed perception - story-wise it may have been only a few minutes, while IRL it was more like a dozen. And I don't agree with a defense "but that's how PnP works" - in PnP we are forced to do turns because of the limitations it implies, nobody imagines the fight we have as they happen at the table - we all imagine it happen about at the same time. Most accurate representation of this imo would be pure RT. But this is where digital limitations come in - first the fact that game needs to be playable in single player mode, next that we need to use UI and controls to process and react to what's going on (as opposed to just "being there" and naturally swinging sword/casting spells as it happens more naturally in our internal narrative). For this reason we do need pause and AI - one to provide us with time to interface with the game and another to substitute for the lack of DM and fellow adventurers. Imagine playing DnD, but it's just DM and you, playing 4 characters at once. What an awkward game of DnD that would be! Overall, TB just feels like a chore for me that I begrudgingly power through to continue with the story. I still wouldn't turn it down to story difficulty because I want challenging fights now and then, when and where it feels appropriate, but I can't help but feel that it's just there to artificially put metaphorical spokes into my metaphorical wheel of story progression.
Despite above being pretty much how I personally feel abot TB, I think a lot of RTwP fans feel similar on what I've described.