Before asking why the imperial system is so illogical it should be remembered where it came from. Originally before the nineteenth century standards as we know them did not exist. The English system of weights and measures were conceived to make trade etc. easy for a largely illiterate population. So each trade had its own system and each district or town had a local "standard" that could be used to check any suspicious weights or measures.
From the Roman mile (one thousand steps for soldiers on the march) to the sheep's fleece (7 pounds) the barrel, hogs head etc. all meant something to the people who used them. Some still remain with us even today Carat (used for gem stone measurement) Hand's used for horses height, Timber measures to show how much useful timber can be taken from a round log all these were devised to suit a specific purpose. The Acre used for land measure (the amount of land needed to produce a given quantity of crop) etc. etc.
Then engineers and philosophers started to look for a standard that could be used for their work and that is when things get interesting. In Britain Joseph Whitworth was responsible for the first truly scientific definition of the inch. He applied this to the threads that still bear his name. The thread angle and pitch was carefully chosen to suit the iron or steel materials available in his day. He did not have access to the high tensile steels we are used to.
The French were responsible for the metric system which was devised on a "scientific" principal involving one degree of arc of the earth at the latitude of Paris. This attempt which was somewhat better than previous systems but even this was not perfect. All that remains of this standard are the names. The current metre was defined by the International Standards Organisation and was applied through out the world, even the "metric" countries had to revise their systems to comply since they all had slight variations in their previous standards.
It may be interesting when talking of logic that the French also tried the decimal week consisting of ten days. It was not a success.
Curiously enough even the metric French still cling to their old measures for wine. Think Magnum, demi-john etc.