You say that 'there are not 100's of different engines' -> but there are 100's of different engines, even within the same manufacturer and in spite of the core being the same it is often extremely hard to swap an engine of the same basic geometry because of the different sensors, bolt patterns and so on. It would be trivial to require those bolt patterns to be standardized and for ECUs to be standardized to the point that they could be swapped between vehicles. It is the - in my opinion ridiculous - differentiation that leads to vendor lock-in resulting in the fact that even though the underlying component is supplied by Bosch and it is absolutely identical you still can't move it from one vehicle to another because they spliced a different plug onto it and other lock-in increasing tricks.
The automotive world is full of such bullshit and given that there is no need for it (wouldn't it be nice to be able to swap an engine from any brand into any other based on a generic form factor and standardized interface) it is clearly all about protecting the profits.
When you go to a VAG garage with an Audi the exact same part from Bosch will be 1.5 times as expensive (as will the mechanic that puts it in) as when you go there with a VW. And if you go there with a Porsche the difference will be even larger. And of course there will be tricks to make sure that the cheap parts don't fit the more expensive model. And that's within what is essentially one company, once you go outside of that your ability to swap parts without access to a machine shop drastically diminishes.
That transmission you mention is a great example: you could swap it out in theory, but in practice the manufacturers have made it impossible to do so, parts have their own identity, talk to the ECU using custom protocols and so on.