Your landlord accepts credit card payments and you pay him/her with your credit card? No different than any other vendor. Mine charges like 2% or something to cover costs.
My last landlord waived the fee if we had it set on automatic bill pay (via the credit card), I'm not sure if the peace of mind was worth the loss, but considering rent was 750 dollars, 2% would have only been 15 dollars. They probably pad the rent a bit to make up for it, but 750 for a 2 bedroom apartment was still a pretty good deal for the area at the time.
With the additional 2-3% that is charged, it comes out to about very similar to purchasing the points directly.
Like Amex SPG costs $157 for 5000 points. If I pay my $1500 rent via my Amex but with an additional $50 premium, after 3 months, I have 4500 points for $150, versus being able to purchase 5k points for $157. If I spend $525, I can get 20k points. So it's better for this particular card to put aside the extra fees paid in rent then purchase the points in bulk at discount than earning the points directly.
Ideally, there's a landlord that doesn't assess an extra 2-3%, then it would totally be worth charging rent on a card.
The key is using the right card with the right processor. There are certain cards that earn multiples with certain processors. Personally, I use a card that gives me 3 points per dollar and pay 2.5% in fees… so I'm "purchasing" points for 0.8c per point. Those points are worth 1.5c+ per point, at the very least.
In fact, I just used 75k of them for a first class ticket to Asia. At a "purchase cost" of $600—so I'd call that a sweet deal.