Heib,
I think its great that you are able to draw on that story for inspiration

If we could all step back at stressful times and realize why we do this, this would be a much easier thing to do!
Unfortunately, the role of team leader comes with having to train and retrain people year after year. Its your dedication that is what gets the team through, though. Would it exist without you? maybe. But it wouldnt be the same. Can you still make a great team without those other teachers? Heck yeah. Students will amaze you. They can teach each other, learn from each other and help take some of the load off. I realized last year I was getting stressed. So we spent a TON of time building a REALLY strong leadership team this year, and they are amazing. It was a lot more work on my part, but they have grown so much and I know they are the future of this team, and maybe in a year or so I'll have more time for mentoring!!
As for not spending as much time with the students, I know exactly what you mean. I say all the time that I miss "just being a mentor". I love getting my hands dirty, adjusting the drivetrain, wiring up the electronics, or even programming it. Luckily with my history in FIRST I have dabbled, and often been forced into all different aspects of the team & robot... and that may even be why even with my BSEE, Im a systems engineer. While it is often more fun to get right in and directly mentor students, I've found my kick lately in mentoring mentors, or developing our leaders. Yes I still jump in and tighten chain when there are only 3 of us left at 11:30 at night, or show a student how to crimp wires when their mentor had to leave... but to some degree the team leader has to let the team run, make its own mistakes and learn from them. These last few years I have been little more than just the team leader... I dont get to mentor much, but the interesting thing is because Im one of the ones "always" there, the kids still feel really close to me, and thats where those moments that carry you through come from too!