Same Shit Different Day
It's not that simple.
Certain fights are much easier or much harder on 10m compared to 25m.
If they didn't learn certain fights in 10m HC then they'll spend a good while wiping on it until they learned the 10m HC tactics, even if they already managed to do it on 25m HC.
In the end, every serious guild that goes for realm first will clear heroic in the first week that it's available, so 10 and 25 both get their achievements at the same time. If not, as I said, the 10 man doesn't deserve it.
25 man raids are organized (especially realm first raids). you can't just say "there will be no 25man raid this week, ten of us want to get the 10man FoS, too"
Besides (and this is way more important), we never had separated FoS for 10 or 25 man.
Did you make that up?
Vigil could decide that they don't want to share the FOS or they just want to troll Mythic and they pour all their resources into grabbing that 10 man FOS. I consider that more of a dick move. But if Vigil runs a 10 man Alt group because they like the challenges presented by 10 man and they manage to beat Mythic to the kill, then I'd say they deserved it.
OT: How is there discussion still going on about this? Whichever guild/group gets the FoS first deserves it.
And like I said before, any 10-man worth their money will not lose their realm first to a 25-man.
Since they introduced shared lockouts there's been a constant statement of "10 and 25 mans are their own race!" so now when we finally get separate FoS to commemorate the end of both races we're seriously finding a way to complain about it?
Fights are pretty much the same mechanically on the two sizes it wouldn't be hard to adjust, the only fight that would differ greatly this tier and need to be relearned would be Dark Animus.
Organisational fights such as lei shen and ji-kun tend to be easier on 10 man, and since the 10 man encounters are tuned for a lower ilvl since the average ilvl of a 10 man guild is lower many encounters could be brute forced since a 25 man guild should overgear it, a 25 man raiding guild probably has a roster of around 30-35 members so if a 25 man guild really wanted it they could rotate in and out and class stack on each fight. I'm sure a 25 man guild could quite easily 'steal' the 10 man realm first afterwards.
'Course if Blizz had any sense about them they'd just make each guild only eligible to receive either the 10 man or 25 man realm first FoS, the only loophole I guess would be making a new guild just to snatch 10 man FoS as well, but as someone said earlier it would be a pointless dick move and I seriously don't see the vast majority of 25 man guilds going out of their way to do that
10/25 are not split difficulties, only split sizes.
So no, the OPs scenario will never happen.
Well except on servers that are virtually dead.