Yes they do. Your whole point, I thought, was that they're being paid to do it. They presently take a small fraction of value from every bitcoin. They also receive any transaction fees offered by any of the transactions they are processing, but in practice those are presently (almost?) always zero.
I'm not saying doing things for money is inherently bad. I'm just saying, let's call things what they are.
It's the difference between terminal and instrumental values. It's one of the reason why some people are bewildered by what Tesla or SpaceX is doing - because they're missing the point that for Elon rockets and electric cars are terminal values and the money is just instrumental, while most of the companies we interact with have this the other way around.
On the one hand, I think I'm doing it to help the network, but on the other hand I kept the pitiful few coins I've got thereby, and didn't give them away. Why do I keep Bitcoins? Not as an investment, surely; I think of Bitcoin as more of another currency that I keep some money in all the time, like £ or €, so I can buy stuff when I'm there. But my little Bitcoin mining operation is being run for the purpose of "transaction security auditing" [thanks, qnr!] for the same reason I run a tor exit node: because I want to encourage such things to exist.