This strategy has been followed by many big investors for a long time. However you can buy btc and store it in coinbase wallet and as far as I'm concerned there won't be any problem. In fact i have been using coinbase wallet for many years without any danger. Moreover, hide all your information and especially mail.
I agree with your option. In my personal opinion, It depends upon the ease with which an individual uses it frequently. You can use hard or soft wallets according to your use and how much you invested. Possibly you can use the hard wallet because it is more secure than others. Moreover, the thing that matters here is If you have a lot of capital, you should be concerned about its safety and should buy BTC to gain your earnings.