One potential problem: I don’t know how it is in the rest of Europe, but in France basically all mayonnaise includes Dijon mustard, so you can’t just use it straight in an American recipe. I did usually see at least one brand labeled “American mayonnaise” that did not include mustard, but people would need to be aware of the difference.

I’d be curious to know if mayonnaise more or less always included mustard and it was for some reason stripped out of the recipe that made its way to the US (my guess would be the British having some role), or if mustard was a later addition to the French recipe after it had already crossed the Atlantic.