I receive emails from Schwab and it seems very straightforward -- there is a personalized link sent to your email, you click it and start to vote. It shows how many shares your have, what the questions are along with the board's recommendations are. No login. Probably not the most secure process but very easy and smooth
Robinhood is a brokerage, and should be passing proxy ballots through to you for companies you hold shares in.
It's arguable whether Vanguard should allow this, and whether it'd matter at the end. Vanguard is for retail investors who want to invest their money as cheaply as possible without thinking hard about it. Delivering proxy ballots, even electronically, does have a cost, and would likely make such funds slightly but noticeably more expensive. And to what benefit? After all, most retail investors don't care to vote. If you strongly care about your shareholder voice, the better solution is to buy shares in the company directly.
That said, Vanguard now lets you select from some broader voting methodologies (e.g. Vanguard's default, ESG, or "good corporate governance"). But nothing specific like "good corporate governance, except screw Musk over/always favor Musk".
Vanguard supports accounts that holds mutual funds (most of their focus/business) but also has accounts that can hold individual stocks.
In the individual stock case, Vanguard absolutely has to allow those share owners to vote their shares.
In the mutual fund case, Vanguard is the investor in the shares and Vanguard is the one who should cast the vote for those shares. End investors are invested in the mutual fund, and so could vote on mutual fund proxies, but IMO, should not be permitted to vote on the underlying shares that the mutual fund is invested in.
Vanguard lets you vote if you own individual shares. Vanguard owns the underlying shares for my units of VTI, so they get the votes. I absolutely do not want to vote on every individual stock in VTI.