None of those tests will silently fail. That’s their point for existing. They complain when the code stops operating as the developer designed it to work.

Integration testing is valuable. It just isn’t scalable to the whole code base (because, as you said, it’s slow), that’s why macro tests should be targeted to the parts that can’t be micro tested (10-15%), leaving the bulk of the code to be tested with blazing fast micro tests. Agile Thoughts podcast goes over this during a series on the Testing Pramid, episodes 1 through 8. https://agilenoir.biz/series/agile-thoughts/