For sure... again, it's how it was handled in early editions. If you described your character as coming from a family of builders, who helped create the church in the local city, and if your DM was willing to let that that mean something, then you could riff on that for both narrative and mechanical benefit. Of course, that was true of nearly EVERY skill in the game at that time -- which, while flexible and expansive could also have its perils.
I'm OLD, and I started back at the beginning of all this

So, yeah, I know, 1e even still says "the character knows what the player knows" (unless you use background skills rule, but it has no mechanics attached). And that's basically what I'm saying, you can still do that in 4e! The ranger PROBABLY knows a good bit about bows and arrows, though there's no specific skill covering this. The druid who used to be a farmer can probably tell you all about cows. In any situation where they might need to make a check they can get a +5 (a proficiency bonus) for stuff like that, just tell me what plausibly indicates your character knows X, Y, or Z (and backgrounds from PHB2 are really all about this IMHO). Again, no real mechanics are attached, and 4e's system will let you do this quite painlessly. Nor do you have to spend 'slots' of some sort on this, like in 3.x.
To which is why I liked the middle ground, creating at least a touchpoint for a character's background/professional skills that could be folded into the mechanics of both skill checks and skill challenges.
Yeah, again, I think the existing class, theme, feats, and background are pretty much adequate to this task.
For a revisit of 4e, I'd consolidate further, such as merging Acrobatics and Athletics into a single skill, as well as Diplomacy and Intimidate into a single Influence skill, place Bluff and Thievery under Scoundrel, maybe add another broad skill or two, and absolutely 100% decouple specific attributes from specific skills to allow the proper calling of the what (skill) and the governing how (attribute).
Now, here I'm a bit different. I see the skills more as 'approaches' to how you typically solve problems. So the guy who uses moves based primarily on strength, in a loose sense, is solving problems with athletic means. The guy who relies on sheer quickness and agility is doing 'acrobatic' stuff. I admit, these two are somewhat closely related, but it still feels like there's a decent flavor difference (and I'm not looking for realism, but more for portrayal). In the case of Diplomacy and Intimidate, they are just DIFFERENT approaches! I wouldn't combine them. And I don't see what Bluff and Thievery have in common at all. Someone MIGHT be a 'scoundrel' and rely on a mix of the two, but its equally possible I'm all bluff and I have no thieving skills at all. Or conversely my thieving is right out there in the open and no deception is required. I wouldn't consider tricking someone with sleight-of-hand 'bluff' either, really. The more I thought about it when I wrote up the HoML skill list the less I wanted to change the 4e one.
Seconded! The MC feats were a nice way of doing it, though I would have gotten rid of the feats required to get powers from the MCed class -- just let the player pick 1 of each so long as they have an equal or more number from their primary class. I too would then create follow-up feats that granted more abilities.
(I also am a fan of Hybrids -- some of the most amazing character concepts and fun on both sides of the screen came from those.)
MCing is MUCH MUCH BETTER than most 'charops' and casual players seem to think. Giving the ability to just swap without any cost is actually pretty OP. I know MOST people here will probably not agree, but I know
@MwaO has stated this same opinion. I would agree though that PMC sucks, though there might be a very few specific ones that are OK. Certainly the hybrid rules killed PMC stone cold dead, and its easy to see why.
As with MCing though, Hybrid characters can be quite 'gifted', and there are some fairly obvious build patterns that are almost too good to pass up if hybrid rules are being used. Such as taking a hybrid in Shielding Swordmage if you have INT as your primary. Warlock can be pretty potent as well, as can Paladin. I wouldn't call these characters 'broken' exactly, but clever builds can be pretty interesting...