There are a lot of apps out there that offer both an exchange and wallet. However, only a few offer you total control of your portfolio by giving you access to your private keys. Gemini isn't it.
The US complicates the crypto world with its various regulations. On top of this, different states also have rules preventing some residents from holding cryptocurrencies.
With this in mind, it is understandable that you may not be able to access your cryptocurrencies right away. It can take up to a week until you can do anything useful with your money, except for Gemini.
1. Gemini does not give you the option to claim your private keys.
- Never trust a wallet who doesn't offer to provide you with your private keys. You know why? Because they can't control your money. These companies play with your money too. If you have the keys, they can't do that.
2. Gemini makes you wait another week to withdraw your money because the address you're sending to isn't whitelisted. Right?! Even the worst offenders of this rule only give you a day. Nope, not Gemini. They make you wait a week. Totally unnecessary.
- The only reason one can think of is they want to continue to play with your money. By "play," I mean invest for their own gain.
Here are other by far better alternatives than Gemini:
1. Coinbase - Still the go-to app for those in the US even though there is a waiting period. They're not shady about it. However, they don't give you your keys. In this case, easily forgivable.
2. Cash App - if you use your debit card, you can withdraw your BTC right away. There are limits, but that so you don't get all "Breaking Bad" on them.
3. Trust Wallet - Possibly the best multi-coin wallet out there. Skip this if you're on iOS, but the best if you're on Android. You get to control your keys.
4. Metamask - The best ETH extension for Chrome. Getting there for Android and iOS. You also get to control your keys.
I did not add any links on purpose to avoid any conflicts.
Be careful out there and be wary of apps that make you wait and keep your keys. If in doubt, make a small test deposit.