You'll get a million opinions but really to be strict, a 'trawler' is a fishing vessel but the pleasure boats called trawlers have a distant link to these. I believe to understand the 'trawler style' you have to have some understanding of the history. Here's my view based on watching this genre develop over the past 60 years.
In my view the genre for pleasure craft got a start when William Garden began to design pleasure vessels that were rooted in the west coast fishing boat. However, first design that really hits the modern 'trawler stayle is his 'Wanderer' 42' power boat (
The Wanderer Class Diesel Cruiser ). These are floating definition of what became the 'trawler style'. I suspect that Ken Smith who penned the GB was heavily influenced by Wanderer. Others like Art DeFever also designed boats that were designed to cruise at less than 10kn, many of which had a striking similary to the Garden design, at least in appearance. These made good 'coastal' cruisers in the west where conditions on the coast can be rough and there is no ICW to get away from it.
Two things, again in my view, gave 'trawler style' a big boost. First in the mid-60's American Marine introduced the Grand Banks. While the GB is in fact a planning hull it was optimized to run at 8-10kn with relative modest power. In later years they had the power to plane and eventually they modified the hull a bit to get better lift and speed. But the GB moved the 'trawler' style from custom to production.
The second big boost to trawler style was the energy crisis of the 1970's. Suddenly planning boats were too expensive to operate at a plane, and boats that were optimized to run at 'semi-displacement' speeds were popular. The majority of these were based on some version of a planning hull but with deeper keels (directional stability) and modest power. These included Mainship, DeFever, Monk, Cheoy Lee, Marshall Bros 'Californian', the various Taiwan boats (Ocean Alexander, CHB, Marine Trader etc), and Island Gypsy (Hong Kong yard that had formerly made GB before they moved to Singapore). Most of these also adopted the traditional look. At the same time some of the established US builders introduced new designs such as the Hatteras LRC, Tollycraft 43/48 etc, and the Bayliner motoryachts of the late 70's. Interestingly, Garden actually did influence the Bayliner Motoryachts of the late 70's-80's. While hull designs varied, common factors were traditional look and moderate speed (8-12kn).
So in my view the 'trawler style' is really just that, a traditional look. The style has evolved to include not only the West Coast style but also the North East style. In addition, the pretense of 'trawler speed' has been dropped. Modern 'trawlers' often have the hull and power to do in excess of 20kn, something the old Wanderer could never have done due to its hull shape. But, they still have that nod to a 'traditional' look.