|There's also the issue of mimicking iconic takes on roles in shows. It happens especially with certain character-y women's roles - Audrey, Adelaide, Lauren in Kinky Boots, etc.
But also, I know that in some Broadway shows (Les Mis, for one, but certainly others), casting people will ask singers to specifically audition by sounding like the recording. They're not looking for a fresh take on the song, they want replacements to merely echo what the originals did. That's when shows start to become products instead of live theatre productions.