That's actually a fantastic idea - a multi-coin wallet.
Only issue for me is because of the gigantic size of the bitcoin blockchain, I don't actually use bitcoin-qt at all, prefer electrum, but the idea could still work, as there are plenty of altcoins out there.
So yes, I would use it (for all altcoins). Just have a list of altcoins and allow people to choose which ones they want to use. Include bitcoin of course

Notes taken

A remote server with the blockchain already downloaded for an "instant-on" is a great idea though.
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I'm interested in the idea and the development.
If you are interested in the developpement, PM me with what you would be able to do to contribute!
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Gen wallet is a bad name tho. I keep thinking generate and I come here to say vanity gen already does that.
Agreed, I was thinking maybe Uniwallet or something else.