I disagree with the conventional wisdom here.
The place where the logic used here breaks down is that the banks buy miles and points for much, much less than you can buy them for. An airline or hotel chain might charge you 2-3c per point or mile. The bank is probably paying somewhere around 1c, maybe less. Inside that very large gap, there is room for you to pay a fee, allow the payment processor to make a profit, and still get the miles/points cheaper than buying them.
I'm currently paying my rent with Plastiq (2.5% fee). I think it's easy to get 2.5% worth of value back from the right cards (the value is often more than just points or miles! Some help to achieve status, as well), even outside a signup bonus.
My situation is, I'm using the World of Hyatt card. Hyatt miles can be bought for 1.7c per point when they are on sale, and there is a cap on how many you can buy each year (I max out this deal, so I am unable to buy more points). I generally redeem Hyatt pts at around 2.5-3.5c per pt, so buying them at 1.7c is a great deal. I consider that "true" value too, because I redeem them on stays that I would make anyway, when the cash cost is high compared to the cost in points. (Unlike, say, an international F redemption on a top airline... the ticket might sell for $10-15k, but if I was paying cash I'd just fly J, because F is not actually worth that much to me)
By putting the rent on the card, I immediately get 1 pt per dollar. This, alone, would be more or less break-even for me. However, in addition, for every $5000 put on the card, I get credit for 2 qualifying nights at Hyatt. The first 60 qualifying nights help me maintain globalist status, and at 70, 80, 90, and 100 nights I get a choice of a 7-night suite upgrade or 10,000 pts. If I take the pts, that's an effective rate of 1.4pts per dollar, which is a good deal in return for a 2.5% fee (a little under 1.8c per pt). If I feel that the suite upgrades have more value to me than the points, I can take those and get an even better return. The nights before that are worth even more (I get a lot of value out of being globalist). I also get a free night for putting $15k in spend on the card in a year (although, I would hit that threshold anyway, so I don't count that in my calculation)
Similarly, putting $25k spend on an airline card might get you a PQD waiver, in addition to the miles earned.
The TL;DR is that the value of points, miles, and status is highly subjective. It's not correct to say that paying rent / mortgage / bills on a CC for a fee is right or wrong for everyone. For me, it makes a lot of sense. For the OP, it might or it might not. The question is, what are they getting for the spend, how do they value it, and how does that value compare to the fees paid?