Egg, do you actually know anything about how controllers are made and how they interface with consoles? No? Then learn. You are not some bright flower of a mind that has discovered some grand conspiracy, but rather just an ignorant person who has found some anomaly and thinks it's a sign of the apocalypse. It's like idiots that don't bother to learn ballistics and rocket science before calling the moon landings a hoax.
The reality is much simpler, but technically complex.
First, the PS4 controller, besides having a bunch of different buttons and features, has also changed things considerably.
You already said the PS2 and 3 controller had pressure sensitive buttons. But did you know that the pressure sensitivity is gone from the DS4?
Did you also know that they're using very different, and much more precise motion sensors in the DS4?
Remember that they announced a speaker in the DS4? Also a port for a headset?
Did you also know that the DS3 controller was already pushing the bandwidth limits for a wireless signal with the PS3, one of the reasons of which was the pressure sensitivity? They also had to change the way the data is sent and handled to accomodate all the new things. Now they have higher resolution motion sensor data to send back, as well touchpad input, the upstream bandwidth opened up by killing the pressure sensitive buttons allowed for that. But now there's a lot of downstream data that needs transferring like in-controller speaker output, headset input/output, lightbar information, and newer rumble feedback.
Sure, the touchpad is a gimimck, but that doesn't mean the whole hasn't made a drastic technical change over the previous.
All these things add up to a significant change in the controller. Also, one of the reasons why you buy consoles is that with each generation, you just buy the system and its controllers, and that's it. You don't have to worry about odd system configurations, or sloppy developers forgetting to support one thing or another. The developers get the benefit of knowing exactly what hardware they're dealing with, and can make games that make the best use of that hardware. If they allowed the PS3 controller on the PS4, that solidarity of platform is broken by developers having to fiddle around for players that stubbornly use older controllers without the proper features.
Sorry, but I'd rather have the headset plugged into the controller, a small speaker to get player specific cues, and other functionality like split screen adjustment based off the controller lightbars.
What you're asking is for developers to gut features from their game, and for gamers to lose out on useful or interesting new features just because you can't be bothered to buy a $50-$60 controller for your $400 - $500 game console. Oh wait, you don't need to buy one because one comes with the system, and I severely doubt anyone will be playing with you on the couch.
I like how the OP avoided this answer, which is probably the best answer here. I love it when someone writes a good answer like this and the OP ignores it because he can't refute it or come up with an argument against it.