Admittedly the some languages might make them very hard to do, but the payoff would be so, so sweet.
There are testing modes that are worth doing, and I think should be part of a development process, but shouldn't be run at every check-in. Long soaks of random input property-based testing is like this, for example.
Personally, there's a free software effort where my contribution is running tens of millions of randomized property-based tests each day and registering bugs when failures occur. This supplements and complements the fast tests that all must pass before changes are merged to master.
Even when I was on teams where the general cadence of getting changes out all the way to prod was on the order of a week, we still had changes getting to our beta environments in less than an hour. And that was on a team that wanted mutation testing, so we had it.
Edit: So my point was team mates that were worried about the 6 minutes added by mutation testing there, were the ones that would commit and then constantly refresh the page so that they could "approve" a change as it goes out. I pushed for all approvals to be automated, so there was nothing for them to watch.
Perhaps mutation testing could have revealed the test suite was lacking in a test detecting that bug (for example, a mutation that changed a type from unsigned to signed or vice versa.)