The process shown could work . . . IF the contractor you hire has the skills needed. But, many do not.

If you hire a contractor who has never done this before, you are electing to become their "guinea pig" or 'practice pool' or 'alpha tester'. Do NOT do this, unless you can afford to pay the first contractor for a repair that fails, and the SECOND contractor, to redo your pool.

Or course, if you can find a contractor with DEMONSTRATED PAST SUCCESS at such a repair, that's another matter altogether.

But in most areas of the country, you'd be better off just doing a liner replacement.