It's correct, there are more ions at higher temperature, but it doesn't prove me wrong.
It does, because it's exactly what you said doesn't happen.
But it does happen.
Hydrogen bonds are broken by electric field:
What electric field? We're talking about pure water.
This is probably why chemical engineers can come out after four years and is able to do real work earning an industry's average of $56,850 a year. Whereas chemist requires a master to do any real work and still gets paid less ($53,879).
That's fascinating, I guess, but I don't see the relevance.
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