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Agree regarding pros/cons of extension vs browser.
For me, I think the gold ring is full browser. Imagine fully integrated paid private services: vpn, voip, email, etc.
Also you could just do neat things that would be difficult otherwise, like during a standard ecommerce checkout, generate a virtual VISA on-the-fly (paying in background by LN) for merchants that don't yet support BTC/LN.
The hard thing about all of this is getting this into mobile space and thats where browser+extension may be the winner.