Why are bicycle tubing diameters often metric approximations of imperial measurements?

The decimal sizes such as 25.4 and 28.6mm are not "unusual" sizes. They are actually the standard sizes. You can count on engineers to do the easy and cheap thing, so they use the standard sizes. "Standard metric size" tubing (that would presumably be sizes in a round number of millimeters like 25mm or 30mm) is not really a thing in the world of chromoly tubing, and doesn't practically exist.

The reason the standard tubing sizes are not a "round" number of millimeters is, of course, historical.

Chromoly tubing is not just used for bicycles, and it wasn't invented just for bicycles. According to Wikipedia, it was invented in 1885 and commercialized around 1891. Chromoly tubing was used extensively to build airplanes (and still is for some small airplanes) because it was strong and light enough to displace wood construction, which standard steel was not. The standard tubing sizes were based on inch measurements, because it was commercialized in a country and an era where inch-based measurements were the standard. And these sizes are still the standard sizes today...they were simply re-named to metric by calling 1-inch tubes 25.4mm, 1 1/8" tubes 28.6mm, etc.

If you shop at a chromoly tubing supplier such as Aircraft Spruce or Wick's Aircraft Supply you will find that chromemoly tubing is available in sizes from 1/4" up to 2+ inches, typically in increments in 1/8-inch. This is plenty of choice of sizes for any engineering need. At the small end of the scale, there are also 5/16 and 7/16" tubes available just in case a 1/8-inch jump is too much. These are the only size tubes available. There are no commonly available tubes in "round" metric millimeters.

When countries began the switch from inches to millimeters, it would be possible to start using 25.0mm tubes instead of 25.4-inch tubes. But then you would have to change all of the tube-making factory machines, all the building fixtures for building things, and all the pre-existing airplane and bicycle designs in the world, and even make new lugs for bikes. Even today, there is no justification for doing that just so that we can all have the small aesthetic benefit of looking at "prettier" round number of 25.0 instead of 25.4. Before widespread metrification, there was even less incentive to do it because 1-inch was actually the more standard way of measuring things anyway.