Where have you backed up your iPhone? If using iCloud, that only backs up the app data for apps you select. I believe the backup you have on the MBP is a full backup of the device to use if needed to do a full restore of the iPhone. Others can correct me if I am wrong here.
I see no reason you could not remove the iOS installer if you have already moved your iPhone to 15.x.x.
If you back up to iCloud you can do a complete backup of everything on the phone. Granted if you back up to the computer it will be a quicker restore, but you can still do a full restore from iCloud. It just takes a while to download and reinstall all the third-party apps when you do the iCloud restore. It’s not like I have to restore my phone all the time. Once every couple of years or so when I get a new one.
I use iCloud back up. I’ve got messages going back to 2012 and I’ve been through a few different phones since then. I’ve found paying Apple the extra $3 a month for 200 gigs of space to automagically back up my whole phone and all my photos to the cloud to be worth it, rather than having to remember to plug the phone into the computer, or manually run a wireless back up. This way I don’t have to think, it’s a constant back up.