I'm convinced that unit tests don't usually find bugs. IMO, most bugs are edge cases that were an oversight in the design. If the dev didn't handle the case in code they're not going to know to test for it. Fuzzing is a much better approach.
At my current position I have the opportunity to work with two large code-bases, built by different teams in different offices. One of the projects has ~70% code coverage, the other doesn't have a single test. Exposure to both of these systems really bent my opinion on unit tests and it has not recovered.
The project with high code coverage is basically shit and has so many bugs that we regularly cull anything marked less than "medium" severity as "not worth fixing". This project was written by a team that loves "patterns", so you can find all sorts of gems like Aspect Based Programming, CQRS, N-tier, etc. well mixed into a featureless grey Java EE goo. We get so many bug reports that its someones job to go through them.
The other project with no tests is a dream to work on. Not a single file over a few hundreds lines, everything linted and well documented. Almost no methods that don't fit on the screen, no recursion. No bullshit "layering" or "patterns". I can't remember the last time we had a bug report, since our monitoring picks up any exception client and server side. Every bug I've worked on was identified by our monitoring and fixed before anyone noticed.
Whats the difference between teams that developed these vastly different applications?? I've worked with both teams for a while, and honestly, the engineers that wrote no tests are of far higher caliber. Use Linux at home, programming since they can remember, hacking assembler on the weekends and 3D printing random useless objects they could easily buy. The other team went to school to program, and they do it because it pays the bills. Most of the bad programmers know what they're doing is wrong, but they do it anyways so they can pad their resume with more crap and tell the boss how great they are for adding machine learning to the help screen that nobody has ever opened.
If your developers are great then tests would hardly fail and be fairly useless, and if they're terrible tests don't save you. Maybe there's some middle ground if you have a mixed team or a bunch of mediocre devs??