RTWP forces you to either be good at pausing the game and micromanaging your party, or be good at programming your companions to be effective without your input. That's it. These are the only things that make it more complex tactically. I myself prefer a slower, more thoughtful approach to my characters' actions. Helps the immersion a great deal, by the way, because you have enough time and opportunity to switch between playstyles and mindsets of your partymembers, and make them feel unique and organic.
Slower equals less complex and not more complex. Complexity is having to make sound judgments and choices quickly. Complexity is having to react quickly, even nearly simultanously, to another's actions. If you can take all day to make your decisions, that then that makes it less tactical, less complex, and at the same time incredibly boring and stupid. It's the easiest thing in the world to do something well/perfectly if you have all day to do it, which is also what makes it immersion-breaking because it is completely unrealistic. That's why even in chess, the classic and quintessential example of a TB combat game, there is a timer for your actions if you're playing the game the true and correct way.
And if we're going to use the "It's D&D and D&D is TB" line, then it's also the case that many, perhaps even most, DMs and certainly any good DM will insist their players make their decisions and actions within a certain time limit and will refuse to give players an indefinite amount of time to take their actions. So to keep it more true to TT D&D, maybe what Larian should do is add a timer to the turns for each character.
