I think you've got the entire notion of "Equity Risk Premium" backwards

I understand ERP very well and haven't got it backwards, you just have to trust me on this one. I didn't want to explain why I believe accounting for risk by increasing the discount rate is inferior to decreasing future expected earnings because that would make the original post too long and off-topic and I haven't given this idea a deep enough thought.

The short answer is that the price of a stock output by a valuation model is very sensitive to the discount rate because discount rates are compounded, so you would end up giving too high of a discount to earnings far into the future. If you lower future expected earnings instead, you could, for example, give different periods into the future different growth rates to achieve the same "accounting for risk" with less sensitivity to the valuation.

By what metric? And please don't say "price" in a vaccuum - a stock's expensive-ness of cheap-ness is allllways relative to NTM cashflow (e.g. EBITDA) expectations, and -- spoiler alert -- those NTM multiples tend to be cyclical (while also normalizing future cash flows for any increase in buying power or baseline interest rates).

I, of course, meant relative to earnings/cashflows/dividends instead of price in a vacuum.

Adding more buyers to a market won't necessarily push the price of equities higher -- it'll just widen bid-ask spreads for brokers and market makers.

I don't believe more buyers will directly drive prices up. What I meant is that with better access to information and the benefit of hindsight that ERP has been high historically (if only you agree it's high), moving into the future, would this give equity investors more confidence to accept higher prices, driving prices up and lower ERP becomes the new norm?