You will find that Holocaust denying specifically has been banned by law from a number of European countries for a very long time. And free speech is still doing just fine.
This might not be the slippery slope you believe it is.
The US is somewhat absolutist relative to the global average on this topic (and even the US isn't complete freedom of speech---pornography law exists, as do various extremely tight constraints on pedophilia imagery).
Has the criminalization of such hate speech helped at all with solving the problem?
That being said, a lot of countries in Europe do not have the concept of "free speech" as is it defined in the US.
European countries were never a bastion of freedom. That's why nazi germany existed in europe, not in america. I love people bringing up europe as some example that we should follow. They most definitely are not.
> And free speech is still doing just fine.
No it's not. That's the point.
Free speech exists to defend offensive/fringe/hateful speech. Popular speech doesn't need free speech protection after all. If free speech exist to protect anything, it is holocaust denial. Think about it. What good is free speech if it can't protect the most offensive speech?