Yes, I have seen the main keyword get boosted in the SERPs when other h* tags are removed. I have seen this on multiple sites. This is not a rare technique and other SEOs do it too.
No doubt your page also can get ranked using the normal h- hierarchy.
The point of this technique is to put as much value on the main keyword as possible. Make it really obvious to the search engines what your page is about. Your page may have other requirements, so use accordingly.
In my experience, I've seen the opposite. Well done h2s in fact, can really boost a series of site's rankings.