ANd how do you use background without skills? Just say "I was an X so I can do it?" (Ok, thats generally how it was done in 2E).
Well, in my case I used my background to shape the plot of the game and much of the flavour of the party's activities. This is a frequent and important (IME) function of background in an RPG. It helps shape the story.
Skill points for background skills are mostly tangential to this. For example, in my current RM game (a system in which there are ample points available to develop "secondary" as well as "primary" skills) I have two PC crafters, one a smith, the other a cook and brewer. The smith's abilities come into play quite often, because the player works at it. The cook's don't, because the player makes no effort to bring those abilities into play.
And even in that game, the more interesting uses of background are not mechanical but rather to shape the plot (eg as players call in favours from patrons, build alliances for their clans, etc).
So whether or not background skills are present, in my experience it is player energy and engagement in the story that matters more.
Now, if you play a game in which the players sit back and expect the GM deliver the story to them, and occasionally use their background to try and tweak an extra bonus against the GM-stipulated challenges, I can see why you might think that background skills are essential if background is to matter. But in my experience that's not the sort of play in which player background matters all that much anyway.
The problem is that 4E still is a rules heavy system so heavy rules light background skills don't fit as they are not equal to the rest of the system.
Is this meant to be a criticism of Skeptic's suggested mechanic? If so, I don't follow it.
I also have to say I don't really get what you are looking for from a system for PC backgrounds. Do you want backgrounds to matter to the story? As I've explained, that doesn't necessarily require skills. Do you want backgrounds to matter mechanically to action resolution? Then Skeptic's sytem does that. Do you want a game in which there is a mechanical substystem for determining how many horses each PC can shoe per day? Then I don't know why you're playing D&D - even ultra-simulationist and gritty games like RM and RQ don't try and answer that question.