"Marketing made me do it" is so unsatisfying in many respects as an answer, though I fear I have mostly anecdote/speculation to add to the question.
Personally, the key addition that digital displays/interfaces add over mechanical dials is precision. While the difference between 2m30s and 2m40s isn't much for a ready meal, if you are looking to soften butter the difference between 3s and 13s is HUGE and will leave a molten mess to clear up!
In addition to the standard imprecision when looking to select a specific point on an incremented scale (on the line vs between the lines vs somewhere around it..), anecdotally the older microwaves I've used have an issue with them not actually stopping at "zero". Following years of manually forcing the dial back to zero, springs/dials/internals have stretched and/or moved out of place leading to the what's on the dial not actually matching what it in supposed to represent.
Once digital microwaves with a keypad to select the time became possible, years of development has led to the introduction of pre-set options for various foods. This seems, in my opinion, to have driven the development of significantly hamstrung UIs.
To summarise the above, I am convinced that analogue/mechanical interfaces are no longer ideal and cannot cope with the additional features built into newer models. Unfortunately, they no longer " do a few things well" and instead have veered into "doing lots of things to a mediocre standard".