While I am not 100% sure, most likely the license is embedded in your firmware. They started doing that with Windows 8.
You can find it out using Linux:
sudo hexdump -s 56 -e '"MSDM key: " /29 "%s\n"' /sys/firmware/acpi/tables/MSDM
Now, it is true that there are pre-activated keys for OEMs disks like HP, Dell, etc.. At least for Windows 7 it was like that. They have so called SLP Keys (System Locked Pre-Installation Key) and they are not the same as the one printed on your Windows 7 machine. SLP keys only work on a certain range of machines, but also have the advantage as working like generic OEM DVDs. I've had this case where a Windows Vista machine (Vista Key sticker) from Dell and I used the a Windows 7 Dell OEM disk, and ... it activated itself. Technically it didn't have the rights to do so and I was totally surprised it did. Use the same OEM disk on an Acer and it will install but not be activated, at which point you use the sticker on the machine. When I started to mess around with these things, I realized that in the Windows 7 era, all machines shipped with two keys: the SLP license and the (recovery) sticker license.
Given that from Windows 8 on the licenses are embedded in the firmware, this is over.
Personally, I think reinstalling from scratch is always the right option. With decrapifying you might miss something, and if you're routined, you have a reinstallation done rather quickly. If you stick with big brand machines, getting drivers is no Herculean task any more. Back in the day, oh, yes, I remember... Hard to find, need to use shady places, take drivers from different machines and try to see whether they work. Today, it's "go to manufacturer website", download what is *missing* and use what Windows gives you as default drivers for all the rest, with the notable exception of the graphics card.