For me, it depends on how satisfied I was with the tires over the past miles and years. I have taken a couple sets of Michelins I was happy with down close to the wear bars, and other brands I replaced much earlier because they didn't inspire enough confidence in winter weather.
It's much easier now to buy a good tire with all the reviews available on line. The Tire Rack is my current favourite site for reviews.
I might go down to the wear bars, but in the past, I've started looking for sales of my preferred tires before that happens.
Years ago, in my impoverished and credit-poor youth, I let a tire go too far and found myself stranded in a remote, rural down and had to spend the night in my car (with my lady friend who was not pleased) waiting for some services to become available. I promised myself that would never happen again.
Down to wear bars and then start shopping. I don't like to go much past that. Also any decent size cracking in them that will catch your fingernail is a no-go for me. My Tercel is about to get a new set because of sidewall cracking.
I find all seasons usually give up wet grip quite a bit before the wear bars, so usually I ditch those with ~4/32 on them... When I can break them loose rolling into the throttle in 3rd gear in my Focus in light rain I know they are done!
I had some BFG sport comp2's and they did well in the wet into and below the wear bars. I never did really hydroplane them, but my commute is on 55mph roads and I have no problems reducing my speed in heavy heavy rain.
Snow tires I retire from winter duty at the snow wear bars, 5/32, but sometimes burn the rest off in summers.
Getting lots of rain this week reminds me why between 40k-50k they are coming off - I like tread depth …
Might also only put 10k a year on them - so between screws removed and/or chipping etc …
Batteries and tires I replace early. 5 years for either really. About 40k miles with my normal driving. I don't find value in getting every dollar out of some things. Nothing wrong with it, just not my bag.
I value my life a bit more I guess and try to avoid needless risk whenever necessary. As a result I do not wait until the wear bars nor "Beyond". Especially with winter tires which get dramatically worse as they wear.
I start looking at replacements when the ride has gotten noticeably rough and the car gets loose pretty easily on worn asphalt or wet concrete. That's usually around 4/32.
Down to 3-4/32, heavy sidewall cracks, or to when they don't hold air anymore or wobble.
I've got a used Toyo that I got with 5/32 and minor tread cracks. Put it on the front of my prius to "finish it off" and it's only at 4/32 12k miles later.
For my personal cars? Until they blow. JK. But they would have to be close, like a bubble that's causing shake or vibration or cords showing through. If it's just worn, I can drive something else if it's raining, no reason to replace yet. For something I'm selling, I make sure they are very good and a matching set if possible, or at least a matching pair on either side of the car.
Wear bars and I start looking. I put a high value on traction in the wet since we get a lot of rain in the SE US and I rarely drive on surface streets.
The last set I replaced had a bulge, worn through the steel belt, and was thumping going down the road. They said 40k, I got 35k. In all fairness it was on the inside which was a first for me.
Wife and kids will get replaced before they pose any reduction in performance or safety.