As I say, I think the current station deceives people into feeling that New Street is in more of a pit than it actually is.
The track is wholly below street level so a classic "concourse on the side and station with a big overall roof" design doesn't work, plus there's nowhere to put said concourse on the side (of a suitable size and with a decent retail offer) without demolishing half of Birmingham city centre. You would always have needed to have the concourse on top and so the platforms would be to some extent bridged over.
I suppose you could do something like Hamburg Hbf, with two retail-filled bridges, one at each end, with an open trainshed in the middle*, but I don't think that would be better, particularly not with a gateline meaning you couldn't cut through the platforms if the retail or exit you wanted was at the other end. (Remember the Bullring exit is by far the busiest and is the one that causes the need to split the A end - you can't realistically get rid of that).
I genuinely think they did the best they realistically could within the constraints of the site and not wanting to shut down half the country's rail network for 6 months to be able to start from scratch. Ban DMUs** from it, clean the ceiling and add uplighters and I think it'd be quite decent.
* Sort of imagine it as it is now, but instead of the concourse where it is you remove the atrium floor so that becomes a trainshed.
** I expect DMUs will be banned from cities at some point anyway; for things like the CAF units they'll need to fit last-mile battery hybrid tech like Chiltern were playing with, and Voyagers just need to go in the bin by then. London will undoubtedly be first but I doubt Brum and Manchester will be far behind.