If the iPad screen has been damaged through breakage, the touch User Interface will be fundamentally compromised. The itself screen is a sensor that provides input to the operating system. Consider that a broken physical keyboard or mouse would be similarly unreliable in responding to keypresses or providing input to the connected computer.
A broken iPad screen also presents a potential safely hazard - as glass shards from the broken coverglass may detach from the screen. The Liquid Crystal used within the screen can also leak - this being a skin irritant.
A broken iPad screen should always be replaced of you intend to continue using it.
iPad Repair & Service - Apple Support
If repaired by Apple, for reasons of practicality, the iPad will usually be exchanged for a renewed/reconditioned iPad of the same model and specification - the cost of the exchange being the exactly the same as a repair.
If your iPad is several years old, repair may be uneconomic. Instead you might wish to put the money that would be spent upon the repair towards the cost of a newer model - that will invariably be more powerful and have a longer usable life than an older device that may have limited support for system software updates and battery life.
