You can be too obsessed with status, just like you can be too obsessed with money, and use them for the "wrong" reasons.
But there are things money lets you do that you couldn't do otherwise, like buying a home for your family or bootstrapping a company.
For status, it's the same. Going to X school gives you an easier chance of getting into X company. Knowing X amount of people gives you more opportunities to meet other well-connected people, allowing you to gain more diversified interactions and/or spread your own influence. Having a trustworthy reputation gives people a reason to give you a minute of their time, and sometimes that first impression is all you need to start a relationship or get funding for your company.
Finally, there are things that status gives you that all the money in the world won't.