Homework is useful as a form of revision, if idiots think they can cheat to a better score the university just needs to take away that incentive: 0 marks for homework, all marks on the exam and a viva.

He should perhaps ask students if they want it marked and if they do still provide feedback, but be clear it won’t count for grades as cheating is too easy.

Lazy students will do no work all year then fail. Clever motivated students will continue to do well.

More people will fail till they realise they need to do the work, but that’s just the way it is, it’s the only way to be sure (along with vivas) that students know the subject.

I was an adjunct math professor at a University for a few years and I completely agree with this. There is this propaganda circulating in (and out of) education that testing is not a good measure of mastery, but it 100% is. It's a hard sell for public schools because, as you said, people will fail more.

Math is an even tougher sell because it's largely a service department. It's hard to justify holding non-majors up because they can't pass calc 2. For upper division math though tests are the way.