I don't think there's much of a problem having a different player throw in.
However, at elite level, it's about repetition to ensure you have the same action every time, that you throw correctly every time and to ensure you throw the exact distance you require every time.
That means lots of practice over an extended period of time
It's not like you can chuck the ball to the winger and expect it to just work.
Hookers practice this throughout their entire youth career (at least those that play hooker at age grade).
You often find the ones that transition to hooker late (Tom Lindsay as an example) are the ones that struggle at the lineout the most.
If a winger was to throw in at the lineout, you'd want them to have been practicing it for years before being expected to do it at elite level
And if you then had a hooker in the team who didn't throw in, there would always be question marks as to why.
That player would be unlikely to have an international career and would find their options limited when looking for other clubs.
It's really not in their interest