That 15 minute wait thing is SOP for any vaccination (including, ideally, a standard flu shot). As Brad noted above, it's to keep you in place in case you do experience an anaphylactic reaction. Jab and Go is not a good idea. Fast food, yes, newly developed vaccine, no.
This shit ain't perfect, but it beats the alternative. If they want to hold you for 15 minutes after the shot, let them hold you for 15 minutes. This is medicine as a developing story, not TCM, ok?