What problem does this address?

Currently, when Theme.json is added, the old menu settings (appearance/menu) are locked away to make place for the new menu.

My case is this: I love the templates, I don't like the menu implementation for clients (and the fact they need to manage it inside the template editor). I am aware a better cycle of the menu management is not yet finished. Also i'd prefer to keep the old menu's in existing client sites, and only do the headers (entry-header so to speak) in Blocks.

So, I want to build a block theme with my own menu. But still keep the rest of block theme.

What is your proposed solution?

Let us specify in theme.json settings (or a php theme support function) whether or not to bring back the old menu.

Or better maybe: Add back the menu, when we remove theme support for block-templates.