Bechamel is definitely the mother sauce here, yes. The general Mornay scheme could be called the mother of all cheese sauces, though, and after seeing Escoffier add fish I've never gone without it just harmonises so well and you can increase the total amount of umami because it's backed by more broad-spectrum subtle aroma than cheese alone.

Side note if you're cooking for vegetarians replace fish and veal / meat extract with mushrooms. Different, but hits just as good as the carnivore variant. Never managed a proper vegan version, the milk isn't the problem the problem is limited choice of different sources of umami. It's not supposed to be a yeast sauce, after all. Make Ratatouille instead never had one complain about it.