I agree that having good test coverage across different levels/purposes makes sweeping changes far quicker, easier, and even feasible to consider doing.

Building and shipping the software is perhaps half the work - another half of the work is growing and maintaining the scaffolding to rapidly, automatically and reliably measure the properties of the software that you wish it to have.

It seems no-one here is arguing that YAGNI should be applied to justify not building automated tests.