Well, using an assessment action, you could assess the fact that someone has a consequence. That would give you a free tag. It's the same as introducing any aspect that is on the scene.
In that sense, Consequences can be invoked in new scenes without needing FP's. It requires an action and an appropriate roll: alertness, scholarship, empathy all seem like appropriate skills. It's not really different from introducing any other aspect through a maneuver or assessment, so I don't know if it would play any part in making up rules. If the person is actively trying to conceal the wound, it might be opposed. I'd say the harsher the wound, the more difficult it would be to hide and, therefore, easier to assess.
That said, it's much more beneficial to do a maneuver and tag it for a +2 than it is to assess a tended consequence and only get a +1. So, I'm not sure how often anyone would do that, unless you make that assessment incredibly easy. I've rarely seen anyone assess a consequence on an NPC. Maybe never.
On the other hand, it may be way easier to assess a wound than, say, trip or flank etc...
I think your best bet is to find a benefit from medical treatment rather than change the way a wound heals.
Well, that's what I was trying to do with the last method I presented. The benefit was allowing the healing process to start earlier and to give people a second chance to start it. Which is pretty much how it already works except I also made it work in conjunction with a recovery power and tied it to a roll. I'm not defending it...just explaining what I was trying to do.
You can break a bone and let it heal on its own, but it might heal crooked. Moderate flesh wounds that could use stitches can heal on their own, but there is also a chance they get infected and worsen instead.
You might be able to do that with a compel...but I do like the idea of consequences worsening. Recovery might make it even harder...bones mending super fast before they have a chance to be set. You could always narrate it that the bones re-set themselves magically if you have a recovery power.
I'm not sure there's a smooth way to do it. A compel could have you re-name the injury into something worse, or have the healing process start over if you don't give it a chance to rest - or if you're slogging through a sewer with an open cut cause some kind of complication. I mean, that's kind of what consequences are supposed to do.
Renaming a consequence when you get it mended would alleviate some of the narrative power on a consequence, so I like that. It's hard to say your wound gets infected if it's been wrapped and sterilized, blah, blah, blah... but even then, a compel is a compel: "your bandage comes undone in the sewer and now its infected, introduction of complication x,y,z." Renaming the consequence can take some of the narrative justification away from your enemy. I do like reducing the tag to a +1, though since that reinforces it mechanically. But, as Sanctaphrax says, tags don't happen much after the scene in which the consequence is created, so it'll rarely come up. Which brings me back to my first point in the post.
What we agree on so far:Medical treatment renames a consequence.