By the time you're publicly traded you're not looking to raise money via equity as you have excellent access to loans by that point. You're not talking about a startup that can't get a loan.
Why? If a company prints a single stock then sells it for $100, I would expect the company's market cap to go up by $100 since it now has $100 more dollars in its bank account.
Because the company printing a single stock is already a signal it is worth a little bit less. If you have N stock for capital valuation $V, each stock is worth $V/N. If you emit one more, you basically need either to argue your company total valuation should rise or you dilluted all stock to be worth now $V/(N+1).
The company valuation is not stock price * stock count, which is your confusion, it's more tangible asset + speculative future assets, so the more stock you emit the less they each is worth. Companies become popular by doing stock buyback (increasing each remaining stock individual value).
Market cap, which is the stuff they do for amateur and children, to multiply stock count by stock price, is entirely meaningless because it ignores value when stocks were actually transacted and liquidity. If you emit a million stock at 0.1c and then create a marketing fad while locking the supply in the hands of a few and refuse to sell, you create a huge gap between low supply and high demand, increasing the individual price manyfold, arriving at a huge market cap... but you paid nothing for most stocks and a few people paid a LOT for a little. In investment banking we use volume weighted average price to try to get a view of what's the short term intraday value of a stock instead.
Imagine, I dont know, a crypto asset with a market cap of a trillion and a single individual owning 1/21 of the entire asset pool, if this single individual signal just one token sale, the entire market starts selling to people who dont want to buy anymore: what is then the value of considering the market cap ? It can go to 0 tomorrow just if demand disappear. Basically you need to include liquidity, a metric of the stability of the supply and demand, that's why I prefer to look at earnings per share to evaluate a company, it is way more significative of what you just bought. For a crypto asset it's 0 for instance.