Interesting topic. The first thing to know is any issues due to not following break-in would be in the long term, in the form of decreased engine/tranny/diff life, but it's almost impossible to quantify. No demo car ever follows break-in rules, and they're sold as 'new' cars, with full warranties.
Issues commonly related to a bad break-in are increased oil consumption, a 'whiny' differential, to a less extent 'whiny' transmission, and decreased engine life, which is very subjective.
In my opinion, break-in is speficied in the US more for legal reasons than mechanical ones, as some identical cars don't specify a break-in period in Europe but they do in the US. Basically the manufacturer wants the driver to get familiar with the car before going crazy, which is also a good idea for the brakes, clutch, differential, transmission, and engine, but how much (if at all) those components are affected without proper break-in is an issue that's impossible to prove. I mostly follow it because I want to be familiar with the car before pushing it, and also makes me feel good that I'm taking steps to maximize the life of my car overall, since driving in that manner means no gear grinding (for 6MTs), no clutch glazing, no brake squealing (due to glazed rotors), etc.
But what's more important to me is how you take care of the car all the time, like no speed-shifting, no hard throttle until oil is at operating temperature, etc. Good day gang.