I agree with you. It was also my first thought, but then read this comment. “The Shelly wallet seems to include the previous transaction history of my Byron so I assume there is no need to keep it open?” What Should We Do With Our Empty Byron Wallets?
It looks like there is a little confusion so let me clear up what I mean about transaction history. I purchased my ADA months ago in a one time sum. My Byron wallet only had the transaction from the exchange. So when I upgraded to Shelly I have just one entry again and in the block explorer I can trace it back to Shelly and then to Byron so I still have a chain of custody and its the same ADA amount.
I went ahead and deleted the Byron wallet but kept the passphrases in case I ever need to restore for some purpose. I do always wonder what happens to legacy tech after it has completed its objective.