Also, capital is not a scarce resource in the US today. For firms that would be worth investing in but don't have access to capital on reasonable terms, the reason for their lack of access is a combination of incentive problems and inefficiency on the part of e.g. VC firms, not because the capital isn't out there. It's true that a wealth tax would increase the cost of equity, but the Finance 101 strategy of "only initiate a project if the IRR of the expected cashflows is greater than the cost of equity" isn't really meaningful for startups since the future cashflows are so uncertain.
If by "those who need capital the most" you mean charities and not startups, a wealth tax would just incentivize giving more to charities and doing it sooner.