Why simple models

Simple models are a way of being sure of what you know. Like double entry bookkeeping, they force you to deal with reality rather than opinion.
Both Feynman and Fermi made a constant habit of building simple mental models. Feynman especially used it as a conscious technique when confronted with a new problem. His use of simple modelling allowed him to make contributions in several different research fields, and he highly recommended the technique. Perhaps his most famous simple model was the o-ring and clamp he dropped in a glass of icewater when he and other members of the Challenger review board were being interviewed. The o-ring's painfully slow recovery of its shape when cold was obvious to all, and pretty much quashed attempts to spin the blame away.
This forced focussing on the obvious is a huge benefit in careful thinking, in that it gets around a key drawback to the way our brains work. Simply put, the brain does not use logic. It relies instead on a principle called 'reinforce success' when it was standard military strategy in the USSR. This is a hugely successful way of dealing with the world, but it results in a thinking instrument that ignores or rewrites contrary information, and that has such a backward grasp of statistics that Las Vegas not only exists but is profitable.
Simple models based in scientific understanding allow this imperfect thinking instrument to get past the random associations it has built up and focus on the actual problem. When the system considered is simple enough, conflicts between the model and reality become obvious. Defects in understanding are thus easy to fix. If complexity is not addressed until the simple model is well understood, apparent complexity often is shown to be unimportant, or easy to deal with.
Using simple models gets one in the habit of forcing one's thoughts to conform with physical possibility in a reasoned way. A reasoned understructure for one's knowlege is of immense value in an era where people increasingly try to sway opinion by applying knowledge of the illogical way the brain works. Applied consistently, simple models "enable you to detect when a man is talking rot"(J. A. Smith, 1914)