In order for the DRM to work the DRM has to be put in the game. Origin is kind of a form of DRM, but it's just a game delivery platform if the Game doesn't have DRM embedded in it to talk to Origin. Otherwise it would be trivial to launch it without Origin after origin installed it, and trivial to redistribute it.
It's really not hard to see who the DRM is intended for, and who they're counting as pirates who ether aren't, or aren't the kind of pirates everyone thinks of when talk about piracy. Might give you a clue about how they have these stupidly high "piracy" figures.
First thing to point out is the your legal rights on a PC are rather small when it comes to what you can do. This site and others like to propagate this lie that you can just take the copy of Windows on one PC and transfer it to another. That's actually false for 99% of the licences out there and would count towards Windows Piracy figures. For the small percentage who paid a premium for a full retail copy of windows, and not the one slapped on their PC by the manufacture, and not the cheap Upgrade copy you can, but that is a tiny percentage of the market.
This is the core of how piracy tallies are made off of the older games prior to DRM that just had key's. You install the game, and put in your key. That's tallied as 1 legal copy. You format your PC, or get a new one, and put the key in again when you reinstall. That contacts the servers and the servers tally that as a pirated copy because it already has a legal tally for that key. Not actually piracy, but how are they to know you are the same person, and not a new person. Remember second hand software on the PC is also Illegal, and Piracy by law. Also with the Licence model they can Licence you to only be legaly able to reinstall it a set number of times.
Isn't the PC licencing model grand at removing, and impinging on the right of first sale.
This is the kind of piracy Steam, Origin, and Ubisoft are squashing.
This is why they pressed to go digital with the PC early.
This is why they've tried to crush the Used market for systems.
Not like any of them understand the economics of why the Used Market made the Game Industry recession proof for decades, and the moment the get a lock in eroding it the 2008 recession started to hurt them all.
There is no way to fix it. Live with the hell the PC has all dragged us to, and accept that most were complicit on the journey there.