Why the Royal Navy would try to save Prince of Wales

If Japanese aircraft had not finished off HMS Prince of Wales, would the Royal Navy have scuttled her because she was crippled?

No. If she could be brought to safety, the Royal Navy would tow and stabilize her because a capital ship was too valuable to abandon unnecessarily.

If Prince of Wales remained towable, the immediate aim would have been to reach Singapore and make her safe enough to move. She could then have crossed the Indian Ocean for major repair. The same logic applied to Repulse: damage alone did not make scuttling inevitable when towing, temporary repair, and a route to a dockyard remained possible. The cost of replacing a capital ship strongly favored recovery whenever it was practical.