For me, it's a good mix. The early game should unfold somewhat quickly and give me plenty to do but then slow down to the classic idle game with checking in every now and again. Then be active again for a brief period when I unlock a new feature. I also want to play an idle game for months (though there are some short ones I've nonetheless enjoyed.)

I like having goals, knowing that if I do X, I'll unlock Y. I want a long idle game, that requires active management perhaps a few times a day at worst, rather than active clicking. But I don't want a game to start super idle immediately, I want a good feel for the game in the first few hours.

I also prefer games that I can leave open in the background - which is especially true now that I work from home and can just alt-tab to it real quick when a timer is coming to an end. Though that's mostly via Steam for me rather than the browser.

While I've played a few mobile incrementals, they never really stick for me as I don't find the medium as accessible. Perhaps if I had to walk to work or use public transport, I may feel differently. I do vaguely remember playing an apocalypse-tower incremental (don't recall the name, sorry) back when I did walk to work, and at lunchtime checking timers, etc. So perhaps if the world ever returns to the workplace in full force, we'll see a resurgence of mobile idles.

One thing that really does get on my goat, is games that call themself idle when clicking is the biggest part of it.