Why do we include cost of equity in WACC ?

It’s an opportunity cost. Or in the capital asset pricing framework, this is the return that I expect (at least, this is why it’s a minimum required return), for the amount of risk I’ve put my money on.

If a company that’s all equity financed gives me returns simillar to a treasury security, then why do I continue to leave my money in as part of their invested capital? Even though I’m still getting returns, they do not reflect the risk I’m taking on. And if management fail to give consistently, at least the required returns for the amount of inheret risk, then shareholders will pull out their money and the company may be forced to liquidate.

I agree but it may be considered both, an implicit (opportunity) cost by first instance as company establishing, as business grow and shareholders base is getting larger, it becomes more explicit cost. Dividends are often more expensive source of financing than interests and doesn’t contain a tax shield.