The only thing Robinhood allows you to do, is buy and sell server tokens that are tied to Bitcoin's and Ethereum's price. In other words, you can't deposit crypto because you don't need it, and can't withdraw anything because you don't own any crypto.
I just had a look at their
FAQ page, and it seems that you are right. This basically means that you pay full price for Ether and Bitcoin, while it's nothing more than hot air, lol. On the other hand, most of the average people having found their way to crypto recently, just want to trade crypto, and don't necessarily want the hassle of sending funds back and forth between exchange and wallet. In that regard, it's quite a smart move from Robinhood, which reflects the insane number of registrants their gained due to crypto.
From Robinhood site;
Digital currency held as a capital asset will be taxed as property, and subject to capital gains and losses. Please consult your tax advisor for more information on filing taxes.
Robinhood Crypto will initially be available to customers in California, Massachusetts, Missouri, Montana, and New Hampshire.
Property tax rates;
California; 0.8%
Massachusetts; 1.57%
Missouri; 1.41%
Montana; 0.72%
New Hampshire; 2.21%
I wish every government charged only these level of tax rates. Even if it was 5%, people would declare their holdings and profits out of free will.