Climbing in seniority and respect in the field in which you work is naturally important, apart from anything else it gives people the ability to get more done, and for anyone gaining 20 or 30 years of experience and knowledge about a discipline, I imagine being bossed about by someone 15 years your junior wouldn't be ideal.
How this relates to the career ladder however is an interesting point, since most people will not end up in senior management positions in large companies then where does that leave you if you are in middle age, and have not 'made it'?
Does this make you a failure? Well, I think that knowledge and skill are not the key indicators of who will succeed in their careers, which seems to depend largely upon luck, being in the right place at the right time, sometimes subterfuge, undermining colleagues in order to get ahead, and often ambition and perseverance.
So if you are happy doing what you do, and are considered an 'expert' in a particular field, then your senior management will likely consult with you, rather than demand you to do as they say.
So in conclusion, I guess yes, it is usually good to climb the ladder as it may make your life more fulfilling, but not essential if you enjoy your job and are happy with your life, and nobody should beat themselves up about not achieving career success, as we all really know that life is a bit of a lottery.