It’s actually not completely crazy to say that one should not have Milchigs by meleva Malka (I cannot say I’m makpid but…).Because the only gemorah that speaks about Meleva Malka doesnt say to wash/eat bread. It says that a certain Amora would Shecht an animal an eat it on Motzei Shabbos. So the only mekor in the gemorah is with Fleishigs.
Milchig vs Fleishig was not mentioned in this paragraph only that somehow Hemish foods (Chulent , Kugel, etc) was more “Kadosh” than Pizza because our ancestors did not eat Pizza in Europe