Adequate test coverage is hard without rebuilding from scratch. Hard to expect in a big, old company. Except when a huge codebase have to be rebuild because python2 have to be replaced (one of our software provider is in this case).
It's a purely mechanical process unlike most of the other problems which depend on changing the behaviour of people in different departments and/or with more influence than you.
Adding the first tests can be a slow and painful process.
Now, once you have those few tests? Yep! Add a few tests along the ones for the new functionality every time you touch a piece of code or pick the low hanging fruit every now and again and you can get to a useful test suite in no time.
Unit testing, for coverage (as a vanity metric) can be mechanical maybe, but integration tests are the way more valuable ones (for the most part) and way more complex.