I completely agree with you. It is better to use multi-wallet for security if you have more assets. Access to one of your wallets can be problematic for any reason. Therefore, it is beneficial to share some assets in other wallets. I used to use Coinbase 2 years ago but suddenly I had a problem with my account. From that period of time i am using Binance for trading and holding activities.
If it's a coin holding, I recommend using another wallet and it's better to use a hardware wallet because we can control everything and don't depend on an exchange like Binance. But if it makes you comfortable keeping your coins, it can be done too.
Since the OP wants to invest 200k on bitcoin I think it makes more sense to have at least two wallets, one of them should be a hardware wallet which should hold the majority of the funds and it should be hardly used and the second wallet could be a desktop wallet in which a small amount of bitcoin could be placed in the case the OP also wanted to make a few purchases with bitcoin, whether this is because he needs to familiarize himself with the process or simply because he wanted to buy something with bitcoin.
We assume the bitcoin price is at $20k so he will have 10 bitcoins. He can keep it in two or three wallets. Wallets with more bitcoins are long-term deposits, while other wallets are wallets for transactions such as trading or others. And another wallet to use on the exchange.