"No phone? Are you hidding something?"
This is the modern world we live in. Decades of pervasive privacy intrusion by governments illegally sucking up all the data of foreign and domestic citizens has done this. It's hard to see any way back.
Of course the unsolvable issue is that the agent gets to decide whether you get in or not, instead of following some checklist. (Which means the agents' internal heuristics become the checklist.)
I know of at least one startup that's selling software to list who's browsing a website with links to their social media accounts in real time. The idea that the CBP can't work out exactly who you are on the internet from your passport seems highly improbable.
I have no idea why you think that. Facebook has approximately 1.7 billion users - that's almost a quarter of everyone on Earth. Besides, I suspect that the people who don't have social media accounts are largely the same group of people who don't travel internationally. If you're wealthy enough to be travelling to the US the probability that you have at least one social media account is very high.