If I have a UTXO of any meaningful amount in the future and make a transaction, the recipient can see the change and know to some extent how much bitcoin I have, right?
Yes, just like when you want to buy an item of $50 with a $100 bill, the seller would return a change of $50 back to you, but they know at that moment that you have $50 in your pocket. Coin control is important for privacy reasons and you should use it to select UTXO's that you want to spend. Or you can send the UTXO through a mixer and receive in it in new and unused address before making the payment you want to make.
Therefore it may be prudent to have UTXOs of a decent size for cost savings but not large enough to reveal meaningful holdings.
Different wallets actually does the trick, one wallet can hold the majority of your funds, you would not want to use a wallet hodling 10 BTC to make a small payment to a friend or to by coffee, and another wallet can hodl smaller amount of funds.