Using a Screen Protector after damage occurs is unlikely to prevent the existing damage from spreading - or prevent inevitable touch screen issues that will become increasingly apparent as the crack worsens.
The relative economics of replacing the screen can only be determined by you.
For practical purposes, in lieu of repairing and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. Unless you have benefit of an active AppleCare plan, an out-of-warranty repair while expensive will be somewhat less than the cost of a replacement iPad.
As for out-of-warranty repair costs, Apple offers a fixed-price price repair. You can verify eligibility and cost for your region/country here:
iPad Repair & Service - Apple Support