I waited to see if anyone more knowledgeable might chime in, but since they haven't...
I consulted my Mastering Pasta cookbook. In that book, all the pasta recipes for filled pastas, including Agnolotti, are egg-rich pastas: sometimes only yolks (more rich and delicate pasta, per book), sometimes whole eggs (chewier pasta, per book).
I looked up Won-ton wrapper recipes. They are a very egg-lean mixture pastas.
The book also said that while traditionally, filled pastas use egg-rich doughs, any pasta could be used to make filled pasta, but that you should appropriately adjust the sauce. The author doesn't elaborate, but, I interpret that to mean 'fat pasta, lean sauce; lean pasta, fat sauce.'
And I have read articles and recipes about making ravioli and other filled pastas with won-ton wrappers, so it's been done before.
Total Aside 1: Rinshin, in other threads you've mentioned where generally, geographically you live. I live in the same general geographic area. And you mentioned trouble finding pitted 'Castelventrano Olives'. If you are a Costco member, they carry them in a 46 oz jar. I always have a jar of these, Kalmata Olives and Sundried Tomatoes in the fridge. With these, an impromptou pasta sauce is always possible, as well as lots of other mediterranean dishes.
Total Aside 2: A local restaurant near my 'native' home town serves raviol simmered in stock, rather than boiled, as an appetizer. It's a traditional Italian preperation, mostly for things like tortellini I understand, but obscure in the west. They're wonderful! Light and flavorful.