You might want to look into the Volume and Mass thread, which is on this exact topic.
Incidentally, since then, Toady has taken some steps towards fixing this problem. It's just that, like so much else, it's a very slow process for anything to get implemented in DF.
Also, barrels and minecarts and such are now volume-based, as previously stated. Barrels have a volume of 5000 (the unit of measure is a cubic centimeter, by the way), while large pots are 10,000. (And you can mod even larger pots if you so desire...)
You and I think a lot alike, it seems.
I quickly read through that thread and agree with the need for a robust volume system. Not so much on mass; allow me to explain.
In the thread, you mentioned an example with a copper earring requiring 0.1kg (100g) of copper. While this may be true for copper, what about a gold earring? Platinum? Lead (lol)? Will it still require 0.1kg of that metal to make one earring, even though each of these metals greatly varies in mass? To make that earring, the same
volume of material is required, completely ignoring material mass. 1 cubic cm of copper has less weight than 1 cubic cm of gold.
So what about the single ingot? The volume of a single ingot would vary depending on the material, quantity of material, manufacturing difficulty, and the furnace operator's skill. For plentiful metals, like copper and iron, their ingots could be extremely large (up to 1 cubic meter, perhaps larger) in ideal circumstances. Rarer metals, such as silver, gold, and platinum, would have extraordinarily small ingots (5 cubic cm at most) due to their precious value and manufacturing difficulty.
On the topic of created items, furniture, weapons, tools and everything else, they should be manufactured in terms of volume and not individual, whole number materials. If you wanted to, you could order the construction of a door with 99% iron and 1% gold, assuming doors have a minimum required volume calculated with the above variables for smelting ingots.
Mass does indeed have its place, but not necessarily for manufacturing. Mass becomes relevant when dealing with weight, momentum, force, and combat in general, where it already holds plenty of sway. As it stands right now, mass has (relatively) the least amount of problems with it. Volume, however, is practically non-existent within most facets of the game.