I can understand the recommendation to not use Robinhood but why not coinbase.

If one is nervous to leave it in the exchange it's easy to put on a cold storage wallet.

For essentially the same reasons. It's one of, if not the least private exchange entity. They can, do & have tracked accounts to wallets & transactions. They can, do & have worked directly against their users w/ the DOJ & the IRS. They can, do & have shut down customers access to their accounts w/ no communication. Abysmal customer service. Abysmal track record. Little to nobody outside of the unknowing general public uses coinbase. This isn't just your address & password type thing, this is your assets. Please stay far away from coinbase & robinhood.