Right now there is almost always a person better than you at almost everything. And probably often a machine system too for many human activities (e.g. excavators, automated looms, 3D printers, stamping machines, combine harvesters, railroad track-laying equipment like the song about John Henry, etc.) Yet "purpose" still exists for most people.
True, but what will be the purpose of humanity as a whole? The idea of being like rats in the subway living under a higher society of robots does not feel particularly appealing for me. Robots making our laws, judging us by those laws, and punishing us when we don't follow them, sounds like a dystopia but is exactly what we will move towards when AI turns out to be better at law making, better at unbiased judging, better at policing, etcetera. It won't make sense not to let them govern us.
As for purpose as individuals, even if you're not the best at anything, you can still make a difference today because those "best" people can't do everything. You can still be an important cog in the machine, do research, develop cures, make better products, etc, or simply do your job well. With AI running everything, none of that will make a difference anymore. There will only be hobbies, nothing of any importance done by humans. No big human projects, no Hollywood movies (why waste a billion dollars on something that can be dreamt up by AI for free?), nothing to be proud of. Nobody will even be able to say "I helped build that bridge". You can still write a book, but it will be a curiosity for friends and family because AI books will be unbeatable in the mass market. One page turner after another, as many as you like about any subject you like, perfectly tailored to human desires. Sure, some people will still prefer human written literature but the masses won't. And will we still bother to educate people so they're even capable of writing books at all? Who wants to spend so many years in school if it's basically pointless?
And then there's another worry: what will the AI do? Will it have a sense of purpose? Will it try to achieve great things? Or will it just descend into nihilism and take us with it?