What you are discovering is just one of the shortcomings of using T.M. as your backup paradigm.
There are others that are worse. You realize that you can't boot from a T.M. backup?
Suggestion:
Consider using either CarbonCopyCloner or SuperDuper to create a bootable backup clone. It will not "grow" in size. You can archive older versions of your files if you desire (CCC). You can even clone the recovery partition (CCC).
You won't realize the importance of having a backup clone around until that "moment of extreme need". Far too many posts from others on this forum, who have such moments, and in the turmoil, discover that they can't access their T.M. backups.
With a cloned backup, you just connect it, turn on the Mac, hold down the option key, and keep holding it down until the startup manager appears.
Then, select your backup, and you're booted again -- and from there, you can "attack" the problem-at-hand. Try doing that with T.M. ...