And why AI can't do all that? Apparently it can be a doctor, engineer, musician etc. but when it comes to do the jobs of certain class of people suddenly can't do that. It doesn't add up, maybe sales isn't as impossible to learn and do?

LLMs can certainly make sales faster and more efficient by automating things like updating CRM, prospecting, finding contacts, drafting emails, etc. There's a whole niche industry building AI sales tools now and some of them work extremely well. But in the end you still need human salespeople (often with lawyers backing them up) to close major enterprise deals.

Claude has neither golf buddies nor a business network.

It doesn't play golf at the club with the C level.