Yes, this is all correct. There are three particularly risky parts of your set up.

The first is as harizen points out - you will be unable to verify your receiving addresses. If you are subjected to clipboard or other malware, the addresses you saved to receive to may be edited at some point between storage and entering them to a website/handing them over to someone who wants to pay you. You have no reference point to double check they are correct. This could be mitigated by printing out your addresses and double checking them against your wallet prior to deleting it, and then using your print out as a reference for all future address use.

The second is you are relying entirely on your seed phrase to be able to access your coins. It would be good practice to back it up in at least two separate locations, in case one back up becomes damaged or irretrievable.

The third is entering your seed phrase to restore you wallet. Typing your seed phrase in to a phone or computer is inherently risky as you may have a keylogger or other malware which is recording your key presses. Unlikely sure, but possible. The only way to be 100% sure your seed phrase isn't been stolen is to never enter it in to an online device.

You also don't need to reinstall Green Wallet to restore from your seed phrase. Your seed phrase will be compatible with almost all good wallets, on phone or computer.

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I've never used it, but Blockstream was founded by and employs people like Gregory Maxwell and Pieter Wuille. The wallet is open source and the github is available here: https://github.com/Blockstream/green_android. It's a perfectly safe wallet to be using.