Given that the USA does not provide universally free education and still suffers from degree inflation requirements, no, I don't believe it's a sound argument that free education would make it worse. It will happen anyway, as it is happening in the USA, even if it costs a lot.

At least with free education everyone has the opportunity to attend it no matter your level of wealth or your financial outcomes from it.

That's not the argument I made though. The argument I made is that it isn't any better, isn't free, and as a further point, they'll do away with the free university programs when they cease to provide economic return because it's a mirage.