I completely agree they have to be profitable, but it is possible for both parties to win even if you buy one.You kinda hit on the bottom line with regards to these extended warranties. "Profit" These programs are not about savings for the buyer but profit for the seller. They wouldn't exist if they weren't profitable. So really who wins the end? It's rarely the consumer.
If you buy Honda Care online for say $1k and you have the fuel injector issue out of 3/36. Honda Care covers it. It has been covered in other threads, folks being quoted ~$1200-1500 or so for this repair. You are happy because you just saved money with HC. The cost for Honda to do that work is probably something like $250 for parts and $100 to a tech. These are all guesstimate numbers, but I think you get the idea. If that is the only claim made, the buyer is happy HC covered $12-1500 in work for $1k, but the dealer cost on that work is much less than $1k.
Then of course, there are always the ones that the person never uses the purchased HC and that becomes pure profit for the dealer.