I know what you mean, and I can say that most of the categorization, which may seem arbitrary, reasonably comes from how those items are manufactured and used historically. An example is pipe versus tube; they are measured differently and have differences in ranges of wall thickness, precision and so on, because different needs and processes developed between pipes that carry fluids vs structural tubing. Most but not all people are going to want one category or another based on intended use, and probably have a highly-available size/thickness in mind already, too.
Getting things custom made is expensive, so customers are pressured to use what's widely available. Stocking lots of things not widely purchased is also expensive. These forces have been working for a long time to give us a pretty wide selection that covers most uses.
I know that pipe and tube have different specifications and applications -- that's specifically why I picked this example. But those differences don't always apply to me. I'd prefer a UI with a check box for pipe, tube, or both, because sometimes I want my search to cover both things. Maybe I want to use a pipe as a paperweight or an art piece or whatever. If McMaster could accurately guess what I was going to use something for, my employer wouldn't need me.
Intelligent search of physical parts is something I've thought a bit about before, in a different context. Often times people with a lot of car knowledge can point out interchangeable items that manufacturers don't come out and acknowledge as being interchangeable.
Examples: Oil filters are often differently sized but still interchangeable between models. You can use an Aisin-built airflow meter from a 90s Mazda to replace one in a Toyota, even though they're different housings, and it would work (if not perfectly) because it's essentially the same part with the same electronics. Brakes and suspension parts often interchange across many models, with the possibility of 'upgrading' to heavier duty parts from more expensive models.
Anyway, it'd be great if you could combine a lot of data and NLP to search off-the-shelf parts based on parameters of varying specificity. Anything from "made of metal and roughly x/y/z dimensions" to "shares the same bolt pattern as part # on a joining surface" could be made searchable in theory.
Getting things custom made is expensive, so customers are pressured to use what's widely available. Stocking lots of things not widely purchased is also expensive. These forces have been working for a long time to give us a pretty wide selection that covers most uses.