I believe it's because the weapons are included through EA Play Pro, which is only available on PC at the moment. Console can only get standard EA Play access.
ETA: I've VERY dubious as to whether this will work, as you likely won't be able to install without having access to them through pre-ordering BFV, but you could see if you're able to find and install the "Battlefield 1 Weapons" DLC pack in your platform provider's store. I guess that the worst-case scenario is that you waste 2 minutes of your time checking.
This is the recent thread where it's mentioned:
Missing BFV Enlister Offer DLC Weapons in BF1 | EA Forums - 12124220
The option is there. It just says unavailable
A pity, but that's what I suspected would happen. I guess that whoever made the Reddit post in the other thread either got incredibly lucky with a bug or forgot that they'd pre-ordered BFV.
The other potential but possibly unfeasible option is to try finding someone selling an old pre-order code online. Of course, that is pretty risky as there are a lot of scams out there, so if you do go down this route, tread extremely carefully.
I haven’t found anyone selling a pre order code anywhere. If you find one do tell me
