I think as always in software, "it depends". The author appears to be assuming there are no tests on all of these paths that we will apparently miss when we migrate the code over. If so that is a problem with testing rather than migration.

Also how messy are we talking? I've seen code at a bank where a junior contractor implemented, in reams of code, his own database locking primitives, apparently unaware that the db could handle concurrent accesses on its own.

Rewrites aren't such a big issue these days, this seems a little dated. The real issue where we get painted into a corner now is architectural, say if you went really hard down the microservices route and tried to back up out of it.