As was already mentioned, turn-based combat doesn't necessarily mean it's slow. Temple of Elemental Evil has an option called "Concurrent Turns", which makes it so that everytime two or more enemies have consecutive turns they'll all act at the same time, not one by one.
Temple of Elemental Evil presented solutions to traditional problems that were never adopted by other developers, sadly, despite being a greatly innovative game in the turn-based realm, I think if that game were to have a remaster today that improved a lot of its issues (none of them combat related) it'd be hailed as a modern master piece.
I could see that being a great solution, but I'm not sure how it would work with 5e.
