I find this to be the biggest issue. Specifically, the "best" time to write tests is also when the code is least likely to be stable!
It's easy to think "if we had just started writing browser tests when we had fewer features, we could have kept up with a testing suite". But that means your browser tests are constantly breaking and people just give up on them. The app eventually gets big enough, and has enough users, that you have to bolt on the tests later to keep bugs from hurting too many customers.
This seems problem seems to be way less of an issue with regular unit tests. I guess the lack of changing dom selectors would be a big reason why.