I upgrade all of my cars because I assume that most people do the same and I suppose the natural reaction is to make sure you are not disadvantaged, especially online.
But that's the subtle difference. Mods don't give you an advantage, they simply ensure you are not disadvantaged. I like the Ferrari 512BB for example, fully upgraded it comes out at around 612bhp, Enzo territory. Except it doesn't because that Enzo has also been upgraded by 30% too and is still way quicker. The net result is that pretty much every single car in the game gets shifted up somewhere between 30 and 50 percent in power without necessarily changing the natural order of things but yes, as others here have said, it does change the character of the cars as the manufacturers intended.
I was thinking about how you could get round this without having 2 copies of every car - financially wasteful, more unwanted garage management and restricting with what you can take online with your limited slots. Now I might be mistaken here as I have never set up an online room but I am not aware of the user having the option to determine as room criteria one or both types of class of car in the game, PRODUCTION and RACE.
This would be incredibly useful as every car in the game can be defined as one or the other, you have around a dozen cars that start as the first and become the latter of course.
Now taking this theme in context of the current discussion, I would have an extra categorisation giving you PRODUCTION, PRODUCTION MODIFIED and RACE. You buy a Lotus Elise 111 and it belongs in the first, you stick new tyres, sports suspension and a flywheel on it and it now belongs in the second category, you go to GTAuto and RM it and it now lives in the third category. Either PD in offline events or individual users online can define which individual class or combination of classes qualify - you no longer get daft situations like the Seasonal Race with stock Cappuccinos where you can enter your RM and overtake everyone by the second lap.
So the last part of my thinking on this now, I take my current fully modded 512BB online looking for a similar race and find a 512BB room which is PRODUCTION only. Now of course it is a hassle to deselect parts and you have stuff like Weight Reduction that doesn't come off anyway meaning you can never actually return the car to its original state. So what I would suggest would be a switch in your settings which allows the user to swap between PRODUCTION and PRODUCTION MODIFIED, switch to the first and your car returns to showroom settings, switch to the second and it is back to include all the stuff you have added to it.
It now qualifies easily for both categories of racing, you see a lot more authentic races and PD could use this subtle extra classes differential to create more interesting events. When Time Trials are properly implemented it would allow extra nuance, would the same people who are quickest with a PRODUCTION car also be quickest with the PRODUCTION MODIFIED version on a different time trial class for example.