You don't need to enter a formal team lead or management role to coach / teach younger co-workers.
Leadership also implies that you are responsible / accountable for the performance of your team. Both your team as well as outside stakeholders will look to you for answers. Hence "management is not a promotion". Not everyone is cut out take on such a role, and not everyone is willing to take on such so role.
> Eventually you might master your domain of expertise and solving the same problem again and again for different customers may become boring
Can I pick this apart?
In the short run? Perhaps. In the long run? That's highly dependent on the industry and your role. Sure, the foundational challenges might be the same - e.g. reconcile user experience, content management and data storage - but the surface level solutions and problems are always evolving, which can keep the job engaging as you grow into it.
The "you're going to get bored in 5 years time" argument is value attribution. Would you make the same assertion towards a medical specialist having a long career in liver or eye surgery? Or an artisanal cabinet maker? Or a shoe designer? Likely not.
Then there are specialists in other industries like oil, welding, car body work, paint jobs,... I mean, even hair dressers - arguably - do the same thing year in year out. Many make careers out of those, and many others move out after a few years feeling that the job has stopped giving them value.
Now, the big risk with a job is that it becomes extremely repetitive and there's little potential for agency as a worker to change the job. For instance, nobody gets happy spending 20 years in front of a screen clicking the same five buttons doing micro-jobs or data entry, or banging in the same 20 commands on a prompt for that matter,... But this has far less to do with the particular role, and everything with the work itself.
In that regard, it's arguable that "move towards a leadership role", or even "coach co-workers", are the only career options to move out of job which just doesn't give you pride and satisfaction after some time.
Moving lateral towards another engineering role, inside or outside your current organization, are completely valid strategies as well. Heck, it doesn't even have to be an engineering role at all. It's completely valid to leave the industry and do something totally different, if you have the financial freedom, and/or freedom from other personal obligations, to do so.
Of the young co-workers I've coached over a decade ago, about half went on in IT, and the other half moved towards entirely different industries doing entirely different things with their lives. And that's entirely fine by me if that's what helps them live happy lives.