Mayonnaise is mostly oil and egg, which is kind of more akin to carbonara than Alfredo. That said, it has a sourness that isn’t going to mesh the same way-- basically, vinegar and/or lemon juice, which one generally wouldn’t want much of (if at all) in something meant to be creamy. Main reason I don’t particularly like it as a butter substitute in grilled cheese.

Knowing what goes into things like mayo, ketchup, Sriracha, etc, can work well when you’re in a pinch, though. It’s just harder to control the ratio of sugars, salts, and sour components so you have to offset that elsewhere.