I like your idea of searching the logged-in user's history! That could be handy. Another thing I've thought about is auto-importing all the channels they're subscribed to so they can search within those.
For the first version of VideoMentions Search, I kept things simple with a single "Channel URL" input field, but using their history/subscriptions is totally doable. I'll see if there's enough demand for that.
In any event, I still think that this simple first version has utility. I like being able to quickly pinpoint all the moments when a certain topic was mentioned across all of a channel's videos.
Thanks so much for taking a look, and for your feedback!