If you pay off your debts without paying any interest all the time, you're pretty much a terrible person to lend money to.
The credit card companies also rely on the fact that however organised people thing they are going to be, a good amount of them slip up. Once they have credit, maybe they dip into it, then can't repay it all, or they miss the interest free deadline etc.
Please stay away from credit cards everyone :)
However credit cart companies do like you better if you are the type to 'slip up', mortgage lenders not so much.
OR I'm not in the US. Other countries exist. I'd be surprised if credit companies even in the US don't share the information on "low or no profit users" - ones who religiously pay off loans without paying any interest.
In Canada (home) and the U.S. (current legal alien), there are things called credit reporting agencies (different per country; names like Trans Union, Equifax, Experien). A surprising array of businesses, including e.g. lenders, utilities companies, etc, buy reports from these credit reporting agencies, and also report to them on your behaviour. As far as I know this reporting on you is completely voluntary for these companies (maybe it gets them a price break on the reports they buy, but I think I heard once at an old job that they actually PAY to make reports), but it makes sense in terms of their self-interest, because it disincents their customers from cheating them. Plus, revenge may or may not be game-theoretically advantageous, but you should see how personal accounts-receivable clerks take it when you don't pay.
As mentioned, the reporting agencies will generate reports on you. You can get these for free for yourself (or for a fee if you want convenience). Companies can also request these on you, I believe only with your permission (which of course would be very easy to forge). If you've never seen your own report, you should find the agencies in your jurisdiction, figure out if you're entitled to a free report, and jump through the hoops just to see what it says about you.
The report includes lots of stalkery facts about you, like your residence history, everyone who reported that you paid bills to them, and so on. It'll probably be only mostly-accurate. For example, I've lived in ten places in the last 15 years, and only about half of them are on my credit report. Also, phone numbers I hadn't used in 5 years were still listed as being mine, but being "closed". Weird. It also includes how often, according to each reporter, you were behind on your bills, by how much, as well as the max balance you carried, the average balance you ran, etc. My report says I was once 30 days behind on one of my student loans, which ... <rant about bureaucrats ellided>. You can easily imagine how that sort of summary might be interesting to someone considering lending you money or extending you credit.
Credit bureaus will also generate a single numerical score about you. I dunno what idiot would use this scalar score to make a decision about you, but maybe some businesses do. But businesses certainly aren't restricted to a one-dimensional metric of your desireability as a customer.
Now. As mchanson points out, different lenders may have different goals. Mortgage providers want to see that you're gonna take your debts seriously. Credit card companies might like you better if they know that you do pay in the end, but before doing so you tend to get into enough trouble that you make a lot of interest payments. Whatever. That said, MY credit reports haven't ever had any information on them that could have allowed a prospective lender to notice that I cancelled an annual-fee credit card on month 11, preventing me from paying fees.
This is differentiated quite effectively from what makes a "profitable" customer. Which, I think has something to do with what the OP was alluding to... Generally, a profitable customer doesn't pay the full balance off every month, and is slightly late once in a while. A profitable customer may have a low likelihood of repaying a debt, and the risk may outweigh any potential profit.
Notably, if you're low-risk, you'll find it much easier to be extended credit up and to certain amounts, even if your behavior does not appear to be particularly profitable.
That being said, when you specifically request that someone offer you credit, you increase the potential risk to the next lender. Which is why most of the credit card arbitrage plans require you to make massive bursts of applications at once, and then back off for a while - gaming the fact that it takes time for each lender to report its data back to the clearing houses.
Another anecdote: I have three credit cards that I use for various things (recurring payments, real-life purchases, online purchases) and I pay them in full every month. I have a very high credit score. The credit card issuers are making plenty of money off of me; they get 4% of everything I buy.
(Why do I use credit cards? One, convenience. Two, it's an abstraction layer over my own money. If someone mistakenly charges my credit card, they've stolen the bank's money, which the bank will really want to get back. If someone mistakenly debits my checking account, well, so much for paying rent this month...)
There's also a significant difference here in that in your situation, you would have been providing the rewards and you would have had power to artificially manipulate the value of those rewards (make it harder to win your game without reward points. Here, the author doesn't provide the rewards he is simply stating what offers the credit card companies themselves are making.
At the end of the day, there is certainly still a moral hazard here but it is also a very different situation than the one you described.
It's not 100% obvious where that line lies, admittedly. I run a small side-project site (started as just something for friends/family) that lists checking and savings accounts that are free of "gotchas": free checking w/ no minimum balances, online savings accounts without weird caveats, etc. (http://www.pfstuff.com/checking/ and http://www.pfstuff.com/savings/, fwiw).
But, I also show some AdSense ads alongside some of the pages... which have the bad habit of advertising precisely the accounts that don't fit my criteria, and which I'm trying to steer people away from. Not always, but Google's algorithms rotate in such "bad choice" accounts more often than I'd like. I can ban some of the more egregious "10% guaranteed interest!" type stuff via AdSense's settings, but not everything. Perhaps I should just pull the ads entirely? That'd be the idealist thing to do, but of course would remove the (modest) monetization potential.