So, what would probably happen is that people would die, and the MDR project would be abandoned shortly thereafter. Minor discomforts may not be necessary information, per se, but the loss of such information can probably lead to more dangerous scenarios - where people weren't attending to situations when they were still minor. Where every edge case where that information does matter, would have made a difference, will be given media attention. People already push past their limits and into dangerous waters because they think they should, or they must - making it easier to ignore minor discomforts means more people will keep pushing their limits until it's actively dangerous.
So, to your examples
Slight cold and heat are unpleasant, and not really dangerous. Deadening the senses to detecting heat or cold can be a lot more troublesome. If someone can tell big changes in temperature, but not little ones, you can get a frog-in-boiling-water effect, where cumulative small changes can add up to big ones. So, how about winter - someone just stepping out into snowy weather can tell it's way too cold, even after MDR. Someone wrapped up and layered won't feel the cold acutely, and can still function in the chill. Someone wrapped up and layered with the MDR can't tell when they get too cold, because they're missing the minor discomforts around the edges that says its a little bit too cold, and a little bit colder, and a bit more... and maybe they'll suddenly pick it up when it's cold enough to get dangerous (which is pretty late, they should not let it go that long), or else maybe they'll never pick it up at all, because the heat loss is gradual through they layers and it doesn't hurt, the cold makes them numb at the same time. The same is true for heat - people will have no trouble in slightly warm environments, but outside on a hot day, they won't be getting the constant feedback that will tell them they are uncomfortable... and they may not get out of the heat before it becomes dangerous to them since the build up is gradual. Heat stroke or heat exhaustion are already a possibility, cutting down on warning signs until they're already in the dangerous zone won't help.
Noticing humid or dry air, again, is not a problem when it's just passing through. There is no real way for the body to know it's just passing through that environment, though, at the moment when it's sending the signal, and no way to know whether the brain is going to insist on staying a while. Not realizing how humid or dry the air is could interfere with the biofeedback around hydration (or temperature control), since that is one of the signals used to tell the body to drink more when the air is dry, or that sweat won't cool the body efficiently when the air is already moist.
Itching, now, that's a different sort of problem. First, to lose random itches or tickling you're outright losing tactile sensitivity and deadening your skin a fair bit - your nerves won't overreact to tactile stimulation if you feel everything less, including pleasant tactile sensations... or maybe I mean if you can feel acutely in good circumstances, you can also feel acutely in bad ones, and this is not a tradeoff most will make. Or alternatively you can turn down the ability to feel itching altogether, in which case you are losing medical symptoms - where an itch might be the first sign of a rash, an allergy, a parasite (fleas), or over-sensitivity due to other other medical conditions (nerves or skin conditions). If you allow more severe sensations through, the problem may be found eventually - but perhaps later, wen it's more serious and/or more damage has been done.
Feelings of fatigue... again, you do actually need to know. Because maybe it isn't "useful" if you're not in a position to rest now but you're planning to go to bed early anyway, but actually why on earth would you go to bed early if your body isn't telling you you're tired? Again, it's really easy to miss how tired you are if the body isn't sending signals until it's dangerous. Maybe it won't matter if you doze off at your desk because you didn't realize how tired you were until too late, but if you were driving because you didn't get the signals that "yes, you were tired", until it was dangerous, and also halfway through the drive, instead of in time to maybe make a different choice or hand off the driving while you were still able to concentrate? Its easier to push through fatigue you can't feel, which is fine and easy until it's dangerous and too late because you didn't rest, you didn't feel the warning signs.
Frustration and stress, okay. Again, it's not really helpful in the moment, it makes you less able to act and react when you really need to. Of course, like fatigue, it can have the secondary purpose of reminding the person that they have limits, and to slow down or get out of the situation before it gets bad. Too much stress and frustration means people walk away from the source of their stress when they can... and if it is less than useful when they can't, well, the body doesn't know which you can or cannot walk away from until the pain doesn't stop you! If it doesn't hurt, people won't walk away until they hit overload, and melt down, and possibly have much worse consequences (mental breakdown, chronic health problems, all kinds of fun).
SO in the end a lot of the minor discomforts aren't about minor discomforts, they're about preventing minor things from becoming major. And people can and do push past all kinds of minor discomforts and well into warnings and often enough, into outright danger - moving the bar for what's uncomfortable doesn't change what's dangerous, and it will make those limits easier to push (even when one shouldn't), and harder to tell the difference between when something is minor, or unpleasant, or heading towards dangerous.
Lots of times, with modern conveniences, we don't need to know minor things, and also lots of times we do need to know - and the MDR leaves us no way to know which is which. The body can't know if you're feeling a little bit cold because the building's thermostat is a few degrees off, or because you've been outside long enough your layers aren't enough. The body can't know if you're itching because your skin is twitchy or something dusted across your skin, or because you're having an allergic reaction in a few minutes. The body can't know if you can get out of a stressful situation until it tells you and you don't... or if you will get out before it's dangerous to your wellbeing if you aren't actually aware when you are pushing to the edges of your physical or mental capabilities.
And, a lot of minor discomforts are strongly, strongly related to minor sensations, the ability to feel things at all - getting rid of the minor pains means losing the capacity for minor pleasures. The MDR means loss of physical sensation in general, and few people will trade the ability to feel (even minor) pleasures for the inability to feel (even minor) pains. How much will you sacrifice of the warmth of a gentle touch, or the softness of a fluffy blanket, to avoid an itch or tickle? Or the pleasure of just hot enough tea or coffee warming you when it's cold out? The fine edge of discomfort vs pleasure of spicy foods or strong alcohol, where it is part of the pleasure? How nice it feels to curl up under warm blankets when you're tired? People must lose parts of those pleasures to lose parts of those pains, because feeling the difference is feeling the difference, for good or bad.