Lots of thought and design DOES go into outsole (tread) design. In some ways it requires even more technical and performance consideration as it can have a huge affect on the overall feel and performance of the shoe.
Of course lifestyle shoes may be more style and less technical…
The reason why I would guess that most drawings you see of shoes here and maybe elsewhere are sideview, is likely just becuase thats what designers often show to communicate an overall design. In an designers full portfolio though, im sure you will see outsole drawings. Check Yo’s site for some good ones.
As for a formula or drag/drop, i wouldnt really say that’s the case, at least for the true performance brands in most categorys. Sure, there are some common things, regarding flex groove placement, lug depth, heel roll, etc, but there is lots of variation if you look closely.
I’ve worked on outsoles in almost every category (running, tennis, basketball, trail, hiking, training, fitness, indoor, soccer, etc.) and have to say that outsole design is not as easy as it looks.
Especially, also to consider is that usually the outsole design (rubber) will be done in conjunction with the midsole (CM EVA) and can be done in a number of different assembly methods (ie. double lasted, dual density, etc.) and other parts (ie. air bag, or cushioning insert, TPU shank, etc.) the whole technical package can get very complicated and detaied.
You also need to consider things like outsole thickness with regards to weight, color dams, abrasion resistance, flex and grip to name a few in any outsole design.
Below are few posts from my blog about the outsole design and development process. Dont have the sketches here and the technical drawings isnt available online anymore, but should give you an idea of the thought process and technical considerations.