Your satisfaction changes from being happy that you've polished some nice bit of code to being happy that you've shipped a product and successfully run a group, and gained the admiration of the people on your team and in your company. Competence is it's own reward.
I learned those rules from observing the behavior of group leaders I've worked with/for. There have been a few times (over many years) when I've thought to myself, "My boss is fantastic! I am so amazingly lucky to be working for this person!!" When that happens, I've asked myself, how does he/she do it? And tried to figure out the answer.
There also appears to be satisfaction in cultivating new talent and watching it grow. A friend of mine is at his most excited and animated when he is talking about the new ways his reports have grown as engineers, not when he's talking about this or that technology.
Well, if you keep working on shitty tasks (because you assign them to yourself) and keep being interrupted, only for your product to depend on the hazards of the market, you will get burned at some point if what you ship fails for reasons that don't depend on you or the team and people leave as a result.
I honestly hope it will not happen because you seem like a great Lead, but you can't say this scenario is not a possibility.
Burnout's likely whenever you work really hard on a product that nobody uses, regardless of what your role at the company was. It sucks to sacrifice hard for something that doesn't pan out.
The solution to that isn't to only work on the stuff that pleases you, though. It's to only work for companies that have traction or at least demonstrated consumer demand. It's the founders' job to validate that there's a reason for the company to exist; make sure they've actually done their job before you entrust them with yours.
This happened to me, and is one of the reasons I quit being a manager and went back to being a developer. The product didn't actually fail, but the daily stress of constant interruption and long hours of slogging through thankless shitty tasks eventually wore me down.
Also, I regret not having delegated some of those boring and shitty tasks, since they would have developed skills in my staff (like debugging under difficult environments) that would have made them stronger and more independent developers.
If you don't derive satisfaction from helping your team, absolutely do not become a lead. Between meetings, planning overhead, interruptions, team communication, documentation, and so on you'll never reach the kind of individual productivity you could alone.
A personal anecdote: I have recently discovered I was bored on a job because the tech lead, after working with a dozens of engineers who considered cleanup and simplification tasks boring and wanted to implement new features, stopped parcelling out those and kept them to himself, while distributing new functionality tasks (which I don't personally enjoy doing 40 hours a week) throughout the team.
I learned those rules from observing the behavior of group leaders I've worked with/for. There have been a few times (over many years) when I've thought to myself, "My boss is fantastic! I am so amazingly lucky to be working for this person!!" When that happens, I've asked myself, how does he/she do it? And tried to figure out the answer.