Probably entirely to do with insurance. They can’t dictate to you what level of insurance to purchase for your private vehicle, but they can for a rental.

Why it matters for the party vs a routine work trip… If they are providing alcohol, they automatically are assuming some degree of liability for your actions when you leave the party.

What if you have an accident and total your personal vehicle? You could ostensibly sue them.

What if you have an accident and god forbid kill or injure another? They or their family could sue your employer (as well as you ofc).

A rental and associated insurance coverage will provide them with a knowable degree of financial buffer before they would have to pay damages out of pocket. If you drove your personal vehicle, they have an unknown and maybe nonexistent amount of insurance coverage to help with legal fees and damages in the event of something terrible happening. All because they provided you alcohol.

This is probably about risk tolerance and not about pinching pennies.