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Waves are comments.

They are in a sense, I agree, but if you take waves as short content platform then it'll be better to have such feature. For example inleo #threads appear in profile page under Threads section and it is easy to review thread written. Same should be here.

Good idea

I thing the normal notification does a great job also

At we have a waves section in profile page.

I don't think it's necessary though since we get it as a new comment and we can continue the conversation there

If you quickly need to look at all waves threads, it is a good UX in terms of website UI.

On website, we open waves replies into waves page. On mobile app, we don't have that functionality yet.

For some waves I see replied back in Waves, but mostly it opens in as a regular comment unless I click the parent post.