Short lifetime can be a benefit for anti-Covid medication too. An antibody could cross react with a vaccine and hamper the immune system response, preventing it from launching a proper reaction and creating proper immunity. You don't want the person having to wait for weeks while being vulnerable until they can get a vaccine after a successful therapy with antibodies.

But of course, distribution is a headache.

A person having an an immune system that can be vaccinated with traditional vaccines (including mRNA), while not developing meaningful resistance (such that a second infection isn't serious even if possible) from an infection where they needed antibodies, doesn't seem very likely. And if they were treated with antibodies once, they could probably just use them again, so it doesn't seem important.

Nevertheless, it would still be moderately impractical in the sense that a vaccination immunity should (probably?¹) be more effective than immunity after an infection, but it may not properly develop until the vaccine is administered without (much) antibodies present.

¹ is there any evidence or a sound supported theory that a coronavirus vaccine is more effective and/or long lasting than immunity after an infection?