Never try to compare value to the commodity price of raw gold/silver/copper. It's largely meaningless. If you want to compare monetary values, generally stick to basic goods like flour, salt, bread, etc.
I usually settle on about $50 per GP, $5 per SP, and $0.50 per CP.
If you look at trade goods, you can see things like flour at 2 CP/lb, or salt at 5 CP/lb. That would then translate to about $1 per pound of flour, or $2.50 per pound of salt. You can get it cheaper at a modern supermarket, but it's a reasonable approximation.
Lifestyle expenses start at 1 SP per day for squalid living conditions. That's about $5 for whatever food you can scrounge up, and no place to live. Modest is 1 GP per day. If you consider that $50, that gets you an apartment (~$20 per day = $600 per month) plus food and some other minor costs. In fact, it works out to about $20k per year in basic living expenses, which isn't unreasonable. Aristocratic is at least 10 GP per day, which would translate to about $200k per year in living expenses — the sort of spending you'd expect from someone extremely wealthy.
A rapier at 25 GP would be $1250, which is not unreasonable for a well-made sword, rather than just a display piece. Without modern machinery, it's going to be on the higher end anyway. A club is 1 SP — $5. I mean, it's a club. A quarterstaff is twice that, at 2 SP / $10. Most weapons are in the $500 - $1500 range, which sounds about right.
Your gambeson armor starts at 5 GP → $250. Imagine the cost of a large coat that's thick enough to stop a sword blow, and that feels in line. A chain shirt is 50 GP, so $2500. Starting to get expensive, but crafted armor is always going to be expensive. Plate mail that costs 1500 GP would be the equivalent of $75,000 — an expensive car, or a cheap house. The sort of cost that explains why only nobles usually could afford it.
A carriage ride between towns is 3 CP per mile, which would be $1.50 per mile. If I plug in a random Uber estimate, I get a cost of $1 per mile, so close enough.
Basically, most prices in the book make sense at this cost scale, though there's a few that don't, or have problems. Alchemist's fire, for example, is a one-use consumable where you're throwing about $2500 at an enemy for a tiny bit of fire damage. That's ludicrously expensive for something you might otherwise see as a commoner's substitute for a mage, in a low-magic setting. A book costs 25 GP / $1250. That's a reasonable price in a setting where every single book is hand-crafted, and even paper is rare and expensive (heck, paper is $10 per sheet and ink is $500 per bottle), but often doesn't fit with the relative commonality of books (such as libraries) in many settings. Crafted glass (such as a magnifying glass or spyglass) is also hideously expensive, at 100 GP - 1000 GP ($5000 - $50,000), but that's less surprising, since accurately crafted lenses are horribly difficult to make without modern machinery.
Of course that then leads to the question of, how much does magic affect the ability to make these things, and should that mean they should be cheaper? At the very least, paper should have a much higher demand in a world with wizards and spellbooks. Probably less so for crafted glasswork, as there aren't a whole lot of practical uses for such items (except maybe old wizards whose eyesight is going).
Summary: 1 GP = $50 is a reasonable scale, though it wouldn't hurt things much if you dropped it to, say $20, or raised it to $100. Some of the edge cases might get a bit more noticeable if you try converting from modern costs to game costs, but it's close enough that it doesn't really need to be fussed with.
Oofta said:
As far as the fabricate, I posted long ago that I saw a lot of issues, especially depending on level of technology and how you define "raw materials". Do you need high quality steel? Does it need to be properly hammered into plates or do you just need iron ore, a source of carbon and some other trace metals? I lean towards the former, which along with the expertise of how to make the armor (which takes a master armorer level of expertise) I just don't see it happening all that often.
I'd say yes, you need the raw materials, but no, the materials do not have to be in any particular shape. If you want to make steel plate mail, you need steel — not ore, or iron plus other stuff — but it could be ingots or plates or whatever other shape you wanted.
Basically, if you can describe what you're doing as "reshaping" (ie: trees to wooden bridge), it would work, but if it's "processing" (ie: ore to metal), it wouldn't. You need wool for clothing, for example, not a sheep.