In Calif, we showed "bridle horses" in the 60s and they did the western plesure class. They were collected up, eye level with the wither, gentle arch to neck, nose slightly out, and a very slight drape in the rein, so that you could still rock the bit in their mouth (usually some sort of modified spade or covered roller). They were shown fresh, between hand and leg, which took some skill, and were 15-2 to 16 hands, and often race bred with some TB.
Then two things happened: (1)the new requirement for AQHA judges to only judge 2 shows per year per state meant west coasters started getting out of state judges who pinned more like what they were used to in Tx and points east - full drape split reins (vs reins and romal) and head/neck straight out/no arch, with very slow lope. This was the cutting horse warm-up lope look, which some thought was the epitome of the true western plesure horse. I moved to Colo then, and found out that the slow lope/rein draped to knees was generally a result of horses being ridden all night. This worked with the 14-2 - 15.2 cutting-bred horses, as their strong and compact bodies could just roll along when tired. It did not work with the taller stretchier TB crosses. (2) Tommy Manion started importing the big fancy Calif horses back east for his youth riders, who cleaned up, as they were riding the very best ones ( the West Coast Open Show Circuit Champions like Alisa Lark) that could adjust to the slower gait. This led to a general desire for larger, fancier horses, but not all had that champion horse great conformation, and they fell apart when very tired from riding all night and forced to go so slow. This lead to the drugs, incredible gimmicks, and bleeding of the 80s-90s, so they did not have to ride horses all night, but the horses then sort of drooped down into glazed-eyed peanut rollers, which somehow became acceptable. Many of today's trainers grew up in that shameful era.
It took AQHA 25 years to get back half way, to where it is today. One of the reasons it got better was specialization - the WP horses only do a few closely related events these days, and are smaller again, with more body strength.
In answer to why people want these gaits, that is easy: It is the same as the plodding WB hunter vs the former hotter TB hunter - way easier to ride for people who want to win NOW, and skip that pesky learning curve. If you can write a big check, you can sit on one of these modern WP horses and win, without needing to know how to balance and collect a horse.