Just a couple of theories on the mantle Eb may have had in mind for Harry. Sorry if I hash up any old ground, there's still a lot of threads I haven't been able to read here and I only read about 1/2 - 2/3 of this one.:
The main one I've seen people bring up before is the Gatekeeper. This one makes a lot of sense. Something about the timing and circumstances of Harry's birth seems to make him ideal at whupping outsiders, and while we've never had any explanation of the Gatekeeper's title, one can assume that it's something along the lines of "Keeping the Outer Gates intact." Or perhaps even permitting them to open on occasion, given that the Council has a Blackstaff. I would assume that this is why the Desert Fox has cultivated relations within the faerie courts at least, if not having much further and expansive knowledge of the Nevernever, because he needs to know when big entities are stirring or when someone might decide to play fast and loose with the fabric of reality.
The other one is a replacement Blackstaff. Given that Eb has tremendous personal respect for Harry and also knows that Harry understands perfectly well how to deal with personal temptation and overcome it, this one makes some sense. On the one hand, Ebenezar would feel pained and guilty to have to give Harry such a burden... on the other, who else could he actually trust with that kind of power?
Third one that comes to mind is Captain of the Wardens. This one isn't as absurd as it might seem on the face. For a young Wizard, Harry has whomped and stomped more big nasty supernatural threats than basically everyone except the senior council members. The younger generation of wizards, who now compose the core of the warden's fighting force following the events of Dead Beat, all respect and admire him. The supernatural world fears him. He killed a faerie queen in the middle of a pitched battle, offed a vampire noble in her own house, summoned the Erlking and contained him on his own, whupped all of Kemmler's disciples, raided Arctis Tor with a mere handful of people, became the Winter Knight and he is now the big, bad mofo who murdered the whole damn Red Court. Also, given that few people truly know Eb was responsible for Casaverde, there must be at least a couple who suspect Harry. All that on top of the fact that he's a brilliant investigator, so as the head of the "magic police" as well as the White Council's army, he's uniquely suited to handling basically every responsibility the role entails.
In any case just being able to threaten an enemy that you're going to sic that Harry Dresden guy and his army on them would have most Old World baddies wetting their pants with fear (basically anything short of Ferrovax would get nervous IMO). A truly inspired council would make that move... and therein lies the rub.
The last one...please don't laugh. Well, try and restrict it, anyway. It struck me that maybe Ebenezar saw Harry as somebody capable of changing the Council entirely, of being the Merlin.
Chances of it happening? Very low, right now. Short of, you know, big bad scary apocalyptic events that change everyone's priorities. Such as might occur in a BAT. Amoracchius was entrusted to the original Merlin, Harry has functioned as custodian for two such swords. As mentioned, he's taken on all manner of threats in his young life, has a legendary reputation, a hefty level of power and magic arsenal...and don't forget that he's something of a direct successor to the original Merlin's teachings. The journal Ebenezar keeps that we see in Turn Coat is a long continuance of thoughts and knowledge going from master to student from the big M himself.
Besides which, on a political level, who actually has as many alliances as Harry? The White Court respect him, the Faerie Courts are all over him, The Church are best buds with him and unlike most wizards, he has a good number of mortal contacts - SI might not be as potent anymore, but they're still a whole department of the CPD, and I get the feeling Tilly's going to be pretty significant. Not to mention Marcone. That, and he's actually managed to politically outmaneuever Langtry (if only by the skin of his teeth) more than once now. Oh yeah, and Uriel likes him too.
It's a longshot...but given events up until now, it seems way more likely than it did a few books back. Plus, really it's only what Ebenezar might want for him, not what will necessarily happen.
Have I gone crazy from sleep and caffeine deprivation or does this make some kind of sense?
