"Just do the vulnerable people first" has the significant advantage of being easy to explain and implement, but it does not maximize the speed of economic recovery.

For instance, I'm a vulnerable person because of preexisting conditions, so I'll likely be offered a vaccine relatively soon after approval. But that won't have a large impact on economic recovery: I'm in the home office in a single-person household and don't have any care obligations, so I'm at a comparatively low risk anyway. And I won't change my current behavior until the disease is fully gone anyway.

My thoughts in treating the vulnerable first wasn't because I thought the vulnerable would then be able to go back out to work, but because the vulnerable would be relatively safe the people with no pre-exisiting conditions wouldn't have to stay home to stop the spread.