Job satisfaction as a manager?

Managers are usually paid better than software developers – I’m thinking middle managers here, not the C-level. Why is that when the developers are the ones that actually build the product? You can have developers without managers, but the other way round is pretty pointless.

For a long time I held the following hypothesis about manager’s wages:

Managers earn well because they (should) have a specific set of people skills that are not that common and therefore in high demand.

Now that I’ve been in management positions I’d have to amend for myself:

The high income is in part compensation for not having the satisfaction of creating something yourself.

At least I hardly ever get around to create something myself. The days on which I write a concept or interview a client are highlights but they are few and far between. Growing a team and processes is not the same as being directly involved with designing and coding a new feature. At least not for me. I’d love to be the kind of person who strives solely on supporting others but most evenings I go home and wonder what the hell I did all day. Pushing Jira tickets is not gonna save the world.

I dimly recall being much happier as a web developer. When I look back on the past 2 years, I was probably happiest while building and launching Retr-O-Mat, a private project.
Other managers don’t seem to have that “empty feeling”-problem. Maybe I primarily have a problem with being a Project Manager? Anyway, I’m wondering, what do you other managers draw satisfaction from?

On a related note: I quit my job and starting on August 1st I give myself a 6 months Sabbatical to create tons of stuff and find out what I want to do with my life – Web development? Writing? Consulting? It’s gonna be one big experiment and also:

Wheee! Freeeeeeeedom!