I have always contended that the imperial system of units could increase costs due to how engineers make design decisions. On either system you tend to reach for commonly available increments or standard steps between measurements. In other words, you might think in terms of increments of 1/6 of an inch in imperial and 1 mm or 0.5 mm in metric.

This has consequences that, at a base level, could mean more or less material utilization and at higher levels of analysis affect how structures are designed.

If designing objects with small features, how far apart will an engineer place features when working with each system?

If you are designing bridge, in imperial, do you place diagonal truss elements in, say, 1 foot increments in imperial and 25 cm pitch in metric? Does metric allow for easier optimization in this regard?

Then there's the question of construction standards for buildings. In home building quite a bit of the hardware used is based in the 16 inch stud pitch in standard wall construction, etc.

Not sure if anyone has ever studied and compared standards from the perspective of common design practices for engineers, architects, civil engineers, etc. making design decisions in the context of the standard they are familiar with or decisions imposed by systems of standardization based on these standards.

My solar panels are 2 m x 1 m, which means we had to design a ground mount structure based on that pitch and space rafters on a metric pitch rather than imperial. I can tell you this confused our local building permit office. The plans called for rafters spaced 19.685 inches apart, which, of course, is half a meter. It took a while to make them understand we could not go for 20 inches (which would have allowed them to use standard tables to estimate loads, span, etc.). Measuring half a meter in the context of construction, is, of course, easy, you just buy a metric tape measure and you are done. Using metric dimensions translated to imperial on a plan that requires governmental approval in a place where imperial is all they speak was in a range between comedy and tragedy.

Here's a simple look at how much more or less material one would use when making decisions in metric vs. imperial. For example, an engineer working in metric would choose a 1.5 mm thickness, not 1.59 mm. Her imperial-standard counterpart would reach for 1/16 of an inch. When you compare these two decisions, the metric decision results in utilizing 5.5% less material. This translates into mass, costs, fuel used in transportation, etc.

1/64 = 0.01563 in = 0.40 mm ≈ 0.50 mm 126.0% 26.0%
1/32 = 0.03125 in = 0.79 mm ≈ 0.75 mm 94.5% -5.5%
1/16 = 0.06250 in = 1.59 mm ≈ 1.50 mm 94.5% -5.5%
1/8 = 0.12500 in = 3.18 mm ≈ 3.00 mm 94.5% -5.5%
3/16 = 0.18750 in = 4.76 mm ≈ 5.00 mm 105.0% 5.0%
1/4 = 0.25000 in = 6.35 mm ≈ 6.00 mm 94.5% -5.5%
5/16 = 0.31250 in = 7.94 mm ≈ 8.00 mm 100.8% 0.8%
3/8 = 0.37500 in = 9.53 mm ≈ 10.00 mm 105.0% 5.0%
7/16 = 0.43750 in = 11.11 mm ≈ 10.00 mm 90.0% -10.0%
1/2 = 0.50000 in = 12.70 mm ≈ 12.00 mm 94.5% -5.5%
9/16 = 0.56250 in = 14.29 mm ≈ 14.00 mm 98.0% -2.0%
5/8 = 0.62500 in = 15.88 mm ≈ 16.00 mm 100.8% 0.8%
11/16 = 0.68750 in = 17.46 mm ≈ 18.00 mm 103.1% 3.1%
3/4 = 0.75000 in = 19.05 mm ≈ 20.00 mm 105.0% 5.0%
13/16 = 0.81250 in = 20.64 mm ≈ 20.00 mm 96.9% -3.1%
7/8 = 0.87500 in = 22.23 mm ≈ 22.00 mm 99.0% -1.0%
15/16 = 0.93750 in = 23.81 mm ≈ 24.00 mm 100.8% 0.8%
1 = 1.00000 in = 25.40 mm ≈ 25.00 mm 98.4% -1.6%
1 = 1.00000 in = 25.40 mm ≈ 26.00 mm 102.4% 2.4%

The consequences go beyond the obvious. Here's a real example:

You have to machine a part out of Aluminum.

The part is 0.375 inches thick.

You would think you can just buy 0.375 in bar stock and go for it. You can't. Bar stock isn't flat. You have to be able to take off some material in order to make it flat. You go to Online Metals (no association at all) and see that the next size up is 0.5 inches thick. You are going to have to remove 0.125 inches in order to arrive at your desired thickness. That means you throw away a minimum of 25% of the metal every time you machine this part.

0.375 in is 9.525 mm. An engineer working in metric is likely to reach for 9 mm for this part at this scale. We are not talking about a situation where we tell someone to design a part that is 0.275 inches. The scenarios is one where two engineers are designing parts with similar functionality and each of them reaches for a size based on customary units in each system. This means the part will be made from 10 mm nominal stock and 1 mm (10 %) will be discarded in order to make a flat 9 mm thick starting blank.

Sometimes the thinking goes the other way, with experience you might start with the available material sizes and design parts that fit within the available volume with consideration for manufacturing requirements.

Once you get into large scale manufacturing the differences might not be as significant because with volume comes the opportunity to optimize raw materials, design, etc. My question or hypothesis is more about everything outside of corner cases.