The big win of TTS in my experience is that it ends up being a lot easier to play board games with folks who are otherwise
not big board game players and are not especially comfortable with computers: For people who play a lot of board games (and especially folks who do a lot of PBEM games, either via an engine like board game arena/vassal, a bespoke website like 18xx.games, or actual spreadsheets and email), the 3D interface ends up being a bit clumsy. For people who do not fit into that group, however, it's a lot easier for more experienced players to help you take your turn, explain what's going on, fix broken game states, rewind turns/actions, and implement the same on-the-fly shortcuts/simplifications/workarounds that organically crop up in casual/teaching environments in real life. Anecdotally, it's usually noticably easier for non-gamers to understand the interface of "it's a physics simulation, so just do what you'd do in real life, but by pointing and clicking" than a custom web/GUI interface, no matter how well thought-out or polished[0].
A corollary to this is that there's actually a reasonably high baseline for how good/bad a game can be on TTS: the ceiling on a good web or phone implementation of a game is very high, but a poorly designed GUI interface for a board game with bad scripting can easily become unplayable. On TTS, things usually are never worse than "well, there's no automation and we have to disable snap-to-grid, so we have to move things around by hand, just like you would in real life". Similarly, the amount of time you have to spend learning is bounded by the time it takes to learn the game IRL, whereas for GUI implementations of board games you usually have to learn the bespoke interface in addition to the board game itself. If your group likes to play a huge variety of games, this flexibility ends up being really valuable.
[0] The one notable exception I've seen for this is http://hanabi.live, which is spectacularly good, and frankly a better experience than real life.