We introduced a ton of clover into our lawn 4 years ago and have been letting it self-seed & spread. It's been great.
My boomer-y neighbors don't like it and make comments, but ours is the only green lawn for several blocks because it hasn't rained for shit all summer. Plus we have wildflower areas so we also have all kinds of bumblebees, butterflies, and dragonflies cruising around.
We've tried both clover and thyme, but we can't get them to really take off. But I think we just weren't doing enough at a time and wildlife was eating it all. Our current course of action has been killing sections of grass with a tarp, then planting the clover and our first patch is doing well.
You do need to water it pretty aggressively at first, or be lucky and have daily rain for about a week. ALSO, the first year is kinda underwhelming in general. It really tool off in subsequent years for us. This is our fourth (I think?) year of the clover lawn and it's really nice now.