They are actually quite number of wallets that one can store TONcoin the most popular is the Metamask wallet which is open source and self custodial, while closed sources like Trust wallet, imtoken and even its own custom wallet outside the telegram is there. Some users just choose to do things that are actually strange in terms of securing their funds.
Most of this ban aren’t related to the government hostility to cryptocurrencies but mostly by the telegram its self. Most of the users that usually get banned are those that farm airdrops and they start spamming different kind of groups or channels with their contents and most of them get reported and then get banned.
I have experience using (Telegram-Wallet) at the beginning of my journey in crypto, It's your friend are not exporting the private-key or wallet they're using. Even the service provider you are using telegram, I still remember the wallet usually created by their official project is always have option to export the wallet or at least a backup for the wallet they're using.
All contains your wallet address, none of backup are crazy mate.
I actually agree with you, I was myself although I didn’t used it check out a telegram wallet user interface. The wallet in question was BONKbot which is use to buy, store and sell Solana network based coins. I actually explored the wallet when I saw the report about something of a phishing attack on it and I hit the link and it generated an address for me and also exported out my private key which it stated that I can use on wallet like Solfare. So even if the OP’s friends has gotten is number banned, with a private key back up he can get access to that wallet again and then move out the funds to a more proper wallet, which should have been the case from starting