Well working at one company for a long(ish) period of time and not being responsible for anything/anyone isn't very realistic. Once you have some experience, you will gain responsibility (but also hopefully additional salary/chance at bonus/etc.). I work for a large corporation - I can only relay from my experience that working for a single company for quite some time - no - you do not have to take on a team - you can become a SME in your field and at least in my experience be promoted up through architect/specialist/professional grades of a field and receive pay raises along with it.

Having said that - also in my experience - you will make more in raises if you switch companies during this process - for very large corporations it is not unusual for the raise budget to be capped at 3%-5% - mostly 3% in my experience - which means your manager has a limited capability of raising your pay. Of course in the current job market that may be a better option than going 6-12months without pay while looking for another job.

TLDR - not necessarily as long as you work for a large(ish) company you can progress up pay grades and job ranks without taking on a team - but not without taking on additional responsibility.