I feel like you might be confusing value and valuation. A valuation is what you believe a company would hypothetically sell for.
Selling a non-profit for ... profit... is kind of directly against the whole point of a non-profit.
So I would say thinking of the valuation for a non-profit is weird as hell.
Something like the Salvation Army has value of course. Sure, if you could buy the salvation army, there would be buyers lining up for this well known brand with cash in the bank and lots of donations (or revenue if you want). So technically you could be talking about a 'valuation'. But selling shares of it in the hopes of propping up value and selling it again... like that is just a for profit company.
If you let non-profits do that, that is basically just the end of real non-profits.