Following your logic, most skills can be derived from one or two more basic skills, but that would lead to pretty short list of skills that wouldn't be enough to fill the pyramid.
Lore for example is basically a specialised Scholarship skill. Deceit is a combination of empathy and performance. Investigation is Alertness combined with Scholarship. Intimidation can be emulated by Presence + any number of skills, depending on the way you want to do it.
But what all skills have in common is, that they perfectly represent the magical gumshoe genre.
Survival kind of has an extra role for me. Just because you know how to play a crowd or command a group doesn't mean you know how to handle an animal. Wilderness skills are almost unnecessary in an urban setting, so you can lump it all into one skill, but I believe it should still be there, just to separate those who have hands on experience from an academic. The same kind of goes for Burglary.
I know, that is something that can and certainly should be represented by aspects, but there is more. Burglary could be covered by other skills, but it would cover way more than what burglary does. The problem is, lockpicking can fit both skills, burglary and craftsmanship, but they come at it from entirely different angles. Yes, Burglary's trappings read pretty much like stunts on various other skills, but like I said above, so does lore in regards to scholarship. I would keep it just for the feel (you know, detectives and gangsters 'n' stuff), and (to come back to the topic) don't really see the need for a homemaking skill for pretty much the same reason. Even in the novels, it is mostly glossed over, and in the game, I don't think it is a skill that will get much use. You either gloss over the things that are covered, or you go into detail, but then you can take the original skills for that.
I might not be entirely coherent right now due to lack of sleep, so if anything up there is strange, I will gladly sort it out later.
There seems to be a double standard here to me. Burglary should be kept because it's specific and flavorful enough to be worth redundancy, whereas Homemaker could be folded into other skills despite the fact that including it with other skills makes any such character vastly more knowledgeable about things that have nothing to do with what they would do (remember, Craftsmanship is the skill of making, fixing, and breaking with tools, which makes it the skill of carpentry, metal working, sewing, tanning, construction, plumbing, electrical, engineering, etc.)
Also, I don't agree that Scholarship matches the flavor of the Dresden Files particularly well. Scholarship is such an absurdly wide skill that I wonder how someone could think that a chemist, a forensics specialist, a historian, a lawyer, and a computer programmer would ALL have the same skill at the same level, with only a few Stunts to differentiate them. Performance has a similar issue, though not to the same degree.
Hence why I'm in favor of rolling together the more redundant skills (Survival, Burglary) and dividing the more broad knowledge (read: Assessment/Declaration) skills (Scholarship, Performance). I think it moves the skills in a direction that makes them both more evenly balanced against each other, and allows more meaningful differentiation between characters.
All of Weapons is using tools. So is some of Scholarship and most of Performance. Also all of Driving and of Guns. Just because it uses tools doesn't mean it's Craftsmanship.
The question you have to ask yourself when deciding what skill something should fall under is not "can I justify this as X", it's "should a character with Superb X be good at this". Your suggestions fail that test. Being a great detective should not imply an ability to survive in the wilderness.
If you're thinking of pointing out that Weapons lets you use all weapons and Scholarship lets you access all fields of science, you're missing the point. See, being generally competent academically or with weaponry makes sense. Most people have specializations (stunts) but the field as a whole is something that you can learn all at once.
Except Craftsmanship is SPECIFICALLY the skill of making, fixing, and breaking (generally the assumption of safely, but not always in the case of demolition) with tools. Tools exist for everything, I'm not suggesting that a rock climber needs Craftsmanship to set up a belay or a chemist needs it to operate a bunsen burner. I do, however, think that lockpicking is a very specified form of breaking a lock safely using small hand tools. Your mileage obviously varies.
I don't actually think that Investigation is defined as the skill of being a detective. It's the skill of observation and identification, which is vastly important to a detective, but not the only application of the skill. What else is foraging but looking for and finding edible materials and shelter?
See previous point regarding Schoalrship. I don't think computer programming and ancient history have much to do with each other at all. I agree that computer science and advanced mathematics and physics and chemistry can all have easy links between each other, as well as languages and history and law all having easy links between each other... but not across the ENTIRE field of scientific, medical, liberal arts, and law. That, to me, seems absurd.
That's why I said "in large part."
Yes, you can use it for many different things, but the focus tends to be on getting out there and going on adventures in/with/around/against the supernatural community. Given that, I don't see how a dedicated homemaker would be much more than a flavor NPC. You could build a character around homemaking, but I don't really see how such a character would actively participate in a campaign enough to be a PC.
Every other skill, I look at it, and I can say, "Yes, you could make that your Superb skill and base a PC around it." Homemaking? Unless we're talking about Maid: The RPG, I don't think so.
Charity Carpenter is a stay-at-home mom who happens to be the wife of a Knight of the Cross, and a former sorceress. When her child was abducted, she stormed the gates of Arctis Tor herself to get her back. When her family was assaulted by fae assassins, she jumped in immediately with a nail gun after getting her family to safety. And yet, no one would confuse her with a primary combatant or a supernatural character, nor do I thikn that anyone would doubt that she COULD BE a PC. I really do think that her peak skill was Homemaking, with Fight and Intimidation coming behind.
A widowed grandfather has taken prodigious care of his home after his wife passed away, partly in her honor, partly because he enjoys the work and loves his children and grandchildren and rejoices in having them as company. However, when a band of vampires snatches them away after a visit, his interest in the occult and old army buddies come in handy to track them down and get them back. His home is his fortress, and he's not likely to ignore the supernatural threats in his city after having such a close personal brush with them himself. Homemaking peak with Contacts and Lore and Guns as lower tier skills, among other action man type skills atrophied from his active days.
I can readily imagine a character whose main role in a game is to have a supernaturally airtight home base, the same way a character could have the main role of being the money man or being the guy who knows his way around the movers and shakers of the community.
My game is different than yours. I really like the everyman, Feet In The Water sort of power level, with more or less normal people with normal interests and skills being forced to deal with the sudden influx of supernatural nonsense in their lives. I think Waldo Butters has a lot to do with that.