Because triangles are a fantastic, high-strength shape, that suits the loads a bicycle is subject to. For the vast majority of cases, it’s a very solid choice. We deviate when specific UX requirements are required (city bikes having a battery and a low stepover to suit a variety of clothing, and the motor makes up for additional weight required.
> Is there a solid technical reason for multiple ways to make shoes that connect to pedals?
All of them attempt to address the same requirement, and make different tradeoffs depending on use-case and environment.
> Why are there several ways to shift from your handlebars?
Price points, performance reqs, handlebar setup, environmental (is it expected to be subject to mud rocks and trees constantly?) and weight.
> With the popularity of disk brakes, why don't we have a standard size for pads?
Same as for shifters: the braking compound and design for a race road bike will be really different to what a DH race bike requires.