The exclusion is not being done in an arbitrary way. The fact that it is being done when it not necessary, and there is a reasonable and rational alternative which is used in the real world (and now the BBB) makes it an arbitrary choice.
Let me give you an analogy. You have a table that seats 8, and plenty of food. You have 10 people to serve. One solution is to serve them in two sittings. But instead you decide to serve only 8. The fact that you chose the 2 excluded in a non-arbitrary way (eg the two who were most overweight), does not mean that your original solution was not an arbitrary one.
The fact that the percentage of excluded teams is fairly constant has nothing to do with a preliminary round being a patchwork solution. It sounds like you don't understand what "patchwork solution" means.
While the percentage of excluded teams does converge to 25%, it increases as the number of divisions increase. It is 20% in a 2-division country, and 23.8%, 24.7%, and and 24.9% in 3-, 4-, and 5-division countries respectively. (This has nothing to do with a patchwork solution of course).
The USA and other 5-division countries already have a field of 4096 teams and take the full season. The preliminary round consisting of 2720 teams from the 5th division would be played on the opening Thursday of the season.
The tournament would be enhanced by universal participation where advancement is determined only on the merit of winning your previous cup round - not your league record from the previous year. While, it would not matter much to teams in the upper divisions - who would simply face slightly more competitive teams, it would not harm them or be a wasted week.
It would be better to cut off the cup at a full five divisions, and have a separate cup for a 6th division.
That you are fine with tournament participate not being availabe to every single team is simply a matter of your personal opinion. It has little to do with the actual merits.
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