Paying dividends is just one way a company returns profits - but there are plenty of other ways, such as share buy backs, or reinvestments in the company (thus making future returns higher).
Dividends, like rents generated by real estate, accrue based on the financial performance of the underlying asset. Dividend payout is the only way valuation has any real basis in financial performance of the underlying business.
No dividend = something else is afoot. Most stocks right now are baseball cards.
1)Possibility of issuing dividends means the valuation can't be too low. If it's too low you can just buy it out and issue dividends next year making bank.
2)The the company may hold assets valuable to other (maybe dividend paying) entities. If the valuation is too low they will just buy it out and pay out more dividends.
3)The company may buy its own stock. If the value is too low they will buy a lot of it and issue dividends later at big multiplier.
I am not sure why you're feeling so strongly about that point. It's about the first thing you learn when dealing with equities. If anything paying significant dividends right now means the business is unlikely to grow anymore.
People trade stock as if the companies were yielding something to the stock owners. Many don't. Acting "as if" the company is making those payments -- imputing a price to the stock according to the underlying fundamentals, or some temporally discounted variant -- is a fantasy. It is a symbolic act. An exercise in recursion, anchored in nothing.
The story the market is telling is a very different kind of story, now.