Since there has been a lot of discussion on comments on this question, I'll restate the salient points that need to be answered, though the OP stated most of them in his original question:
What are the consequences of failing to "bed in" a bicycle disc brake rotor?
The consequences of failing to bed in a rotor include reduced braking power, uneven braking power, noisy brakes, reduced lifespan of pads, though not typically the rotors.
In the main, these consequences are long term, though permanent might be an over reach. Though many people feel that a brake rotor "naturally" beds in with regular use, this is a fallacy born of a misunderstanding of the term.
Thus, I will first define the term.
Bed in, rotor: The process of transferring material, either resin or
metal, from a brake pad to the surface of a brake rotor, through heat
transfer, specifically depositing an even, continuous layer of pad
material on the rotor, for the purpose of increasing braking friction.
While normal braking does transfer some pad material to the rotor, regardless of whether the appropriate procedure is followed, that does not mean the brake is automatically bedded correctly, or that the procedure has no point. Bedding in the rotor is intended to apply pad material to the rotor in a continuous and even layer.
This is best achieved by bringing a bike up to speed, and then applying the brake smoothly and consistently to slow the bike, releasing the brake without actually stopping.
Normal braking, which for most people does include actually stopping, if done on a fresh rotor that has not been bedded in, will apply pad material in an uneven layer. Stopping during the bed in period creates a patch of material on the rotor which can cause the brake to pulse or grab during braking. Uneven braking is the second consequence of failing to bed in the brake. This is relatively long term, lasting at minimum until the rotor is cleaned of the pad material, new pads are installed, and the bed in procedure is performed.
The first consequence, which is short term, is the lack of braking power and control. On a new set of Shimano Ultegra hydraulic discs, until the brake bed in procedure is performed, the brakes essentially fail to stop the bike. While they create some drag, the wheels do not lock up, and there is no modulation. After the mechanic installing the brake performs the bed in procedure, their performance is quite good. The difference is quite obvious to anyone who has ridden these brakes in both states. This is unlikely to be an issue in the long term, unless the bike is ridden in a location or at a speed which puts the rider at risk, prior to bed in.
The third consequence, reduced pad/rotor life, is minor, and not typical, though it is mentioned by the manufacturer as a possibility.
One additional benefit of bedding in a brake is that it "trues" the mating of pad and rotor, causing the alignment of the pad to the rotor to be more precise. This has 2 primary benefits, that of silencing the brake, as the "squeal" that is typical on a new disc brake is usually caused by vibration due to the minor misalignment between pad and rotor causing "chatter" between the 2 surfaces. This portion of the bed in process does also occur through natural braking, and is the source of the fallacy that bed in will happen naturally.
The second benefit, increased brake modulation, is the result of this trued mating allowing finer contact between brake pad and rotor, due to finer tolerances in the mating of pad and rotor.
This is not to say that bedding in a brake is a life or death issue. Many people have ridden new brakes without setting them up correctly, and been just fine. But that doesn’t mean that their experience with their brakes gives them the best possible performance that they could have gotten, with just a bit more care and time during setup.
As for the idea that a BSO with disc brakes not being properly set up should set the standard that all bikes are built to, that’s a false argument. In fact, I guarantee you that the owner’s manual for that BSO says that the bike must be assembled and tuned by a professional before riding, and that the professional in question must follow the manufacturers’ recommendations when building the bike, including those for brake setup.
The fact that it is not cost effective to have a professional spend $100 worth of his or her time on a bike sold for $100, doesn’t mean that it shouldn’t happen.