The argument of what would be better if we started from scratch will hopefully never be relevant since most of us are in nations with multiple cultures.
> cultural purity
What next no-argument will you show up with, Rasenwahn of the Third Reich or Eugenics?
The OP said that
> the argument for a homogeneous culture is easy to make
and you end the discussion by speaking of the devil and the devil shows up?
Some people want to keep their culture, so you can either force them to change, move them, kill them, or stay multicultural. To avoid being terrible you just have to let others be and trust them even though they are different.
I don't believe I'm exaggerating that cultural homogeneity is a really ugly idea with a terrible history and it is hard to make an argument for it on a national scale.
The U.S. used to do it to a certain extent. It was a part of the process of becoming American by joining the "melting pot" of cultures and becoming genuinely American. The idea of multiculturalism in America is relatively recent.