Would random sitting arrangement be the best way of boarding for passengers?
The Mythbusters tested various boarding patterns in their previous season (see the digest here, full episode here) and came to the conclusion that "random-random" (close to Southwest-style) was the fastest way to board (though the least liked), and that the current most common method among traditional airlines (back to front) was the slowest. Alternate styles including two forms of "WILMA" boarding (Window-Middle-Aisle, United does this) and "Reverse Pyramid" style (which U.S. Airways used to use) were both fast and very well-liked by the volunteers. I have some issues with their testing methods though:


They only allowed for a single test of each boarding plan, using the same group of volunteers each time. That means two things:


Order of testing matters, because your group will generally become accustomed to getting on and off a plane, which will speed things up as the day progresses.
Any "noise" inherent in a variable of the test that you are neither controlling nor testing cannot be cancelled out and can skew the results.

They tested the control (back to front) first, meaning their volunteers were totally unfamiliar with the "plane" and thus would be expected to be slowed by inefficiencies born of this unfamiliarity. If no other test were repeated, it should have been this one (at the beginning and end of the day) to compensate for this.
First/business class were always boarded first (this is common but not universal among airlines), while every other ticketed passenger regardless of age was boarded according to their individual seat, with only "lap children" boarding with their parent (airlines nowadays require a ticket and seat for anyone over 2yo, so boarding families with pre-adolescents was not really tested). This is opposed to other variables such as overloaded passengers, guys heading "upstream" to the lavatory etc which they sprinkled in to spice up each boarding experience.


One final thing; boarding faster only means you're sitting in a cramped airliner seat longer. Getting passengers aboard an airplane is usually the easiest and quickest part of turning an airliner around. Unloading/loading baggage, refueling, preflight checks etc all take longer in the aggregate than anything going on inside the cabin.