Oh, I agree that this could be done. It's just that relocating the patients is at odds with quarantine: even site-to-site transporting seems to involve a pit stop at the starship platform, as in "Cloud Minders". Even worse if the "they can't be everywhere" assumption fails and the patients need to be rapidly re-relocated!
But why would shipboard quarantine fail? Even if site-to-siteing to the ship's standard quarantine booth won't work, the transporter room itself can be declared a quarantine booth for as long as it takes to sterilize the place. And this shouldn't be all that time-consuming: we have seen how the crew's utterly lethal sidearms can be fired harmlessly against the ship's inner walls...
Timo Saloniemi
But why would shipboard quarantine fail? Even if site-to-siteing to the ship's standard quarantine booth won't work, the transporter room itself can be declared a quarantine booth for as long as it takes to sterilize the place. And this shouldn't be all that time-consuming: we have seen how the crew's utterly lethal sidearms can be fired harmlessly against the ship's inner walls...
Timo Saloniemi