Relatedly, does a landlord have the right to know when you are in your home? Because that's a side effect of this (which could already be possible by monitoring things like electrical usage). Asking in both legal and ethical senses (which I expect are different).
So the landlord likely already knows which fob's have entered the building at any given time. Presuming that most of the fobs are with their rightful owners, then the landlord knows mostly who is in the building at any given time.
However, I'd wager courts would side with tenants that their right to privacy and ability to distribute a key are more important than the landlord's ability to fight subleasing this way.
The end result of the landlord knowing when you are in your home does not change that.
[1] Same principle that allows you to photograph the police out in public or really anyone else.
In your case, the landlord does indeed have a very hard to search record of your comings and goings, in mine it's an up to the second report.
If you have a camera that has any publicly available (not just public, also private-but-unfenced) place in it's FoV, you must register with your local data protection office and fullfill all the requirements (you must prove, how you use, make available, securely store and dispose any recordings).
If you don't have any publicly available space in your FoV, you must have a written permission from all the co-owners (e.g. in an apartment house).
So basically it is only easy if you are sole owner of the property and only you (and your family) are using it. Anywhere with a shared space, it is an issue. For a landlord, that would get no-go quickly.
I didn't investigate this further beyond my use-case (many co-owners, asking them to agree to anything is like cat herding). Given the protection the renters are getting, I wouldn't be surprised if such a permission would be difficult to get, and the common areas would be considered publicly available.