Why a modeler originally choose 1:144 scale to create a plastic model such as GunPla? Why not choose 1:100 or some other number that can easily determine the size of the model from the original size?
(Didn't you ask this exact question of SF&F yesterday?)
Traditionally, toy makers have used a 1:12 scale when building scaled down model of real objects, such as dollhouses. This practice pre-dates the metric system, and made it easy to scale down measurements because, at 1:12, one foot becomes one inch.
Now, suppose you wanted to build a dollhouse, and inside it, you want to have a dollhouse. To do that, you'd have to scale down your 1:12 model house by another 1:12, to give you 1:144. This is why 1:144 is sometime's called the "dollhouse's dollhouse scale".
Since 1:12 and 1:144 were already well known and popular by the time anime miniatures came around, the first people to make such models were already familiar with it, and they used it. After that, it's mostly inertia.
It is likely an unofficial common standard based on tradition that is used for small models and figures. As キルア said, 1:144 is a natural way to scale down a 1:12 scale model, which is another historically popular scale.
Theoretically, you could use whatever scale you wanted. It could cause compatibility problems if you use an uncommon scale as other figures would not be the right proportion due to being based on a different scale, but it would work just as well in every other way.
Some of the more common modeling scales are based on the Imperial System, rather than the (base-10) Metric System. 1/12 for dollhouses is one foot per inch. The popular aircraft scales of 1/48 and 1/72 are four feet and six feet per inch, respectively. When it came time to produce models of larger subjects, in particular airliners, 1/144 made perfect sense. It is 1/2 the size of 1/72, and still an even division of units in IS (twelve feet to the inch). As a previous answer pointed out, Bandai most likely chose it because it was suitable to the size of their subjects and was already in popular use.
There have been efforts to popularize scales that are base-10, but they've had very limited acceptance; 1/50, 1/100 and 1/200 have all been used by various kit-makers, but none have gotten the customer buy-in that the other scales have. Other Imperial-based scales that have strong followings include 1/96, 1/192 and 1/720, which are popular in boat/ship modeling.
Then things get interesting in the world of scale. (Well, "interesting" if you're a model geek, I suppose.) Some scales don't really make that much sense, unless you know some of the history. While 1/720 is/was frequently used by U.S. model manufacturer Revell for ships (and later Italian manufacturer Italeri), the 1/700 scale used by Japanese manufacturers has become much more popular. And once 1/700 had a lot of appeal, 1/350 (2x the size of 1/700) came along a few years later for people who wanted larger-scale models. The 1/32 scale (3/8" equals one foot) that is popular in aircraft and has some acceptance in automotive and older armor kits, was mostly introduced by railroad modeling. It is also popular with slot car models. It's popularity with armor lost out over the years to 1/35 scale. 1/35 was made popular by the Japanese manufacturer Tamiya, largely so they could fit motorization gear into their models. Their models proved more popular than the 1/32 offerings from places like Monogram, and eventually 1/32 largely disappeared from the military miniatures landscape. Except for the realm of figurines, many of which are still sculpted to 1/32 (54mm) scale.
(I'm sorry... what was the original question...?)