If CBP knows you're a 1P user (which they hypothetically could since the NSA has read 1P's emails to you, a foreign user of that service), but you don't have the app installed when you attempt to enter, what makes you think they'll respond differently than they currently do to people whom they know have Facebook accounts, but delete the app from their device before attempting to enter the country, rather than allow the immigrations agent access to their feed?
You're absolutely correct that there's nothing stopping your proposed scenario from happening. That being said, it's extremely unlikely they'll do that because in order to do so, they would have to:
1) Intercept your emails
2) Store the fact that you're a 1P user
3) Match up your email address to you, as a person at the border
4) Stop you at the border for questioning
5) Force you to unlock your phone
6) Recognize that your phone does not have the 1P app installed
7) Force you to install the app + unlock it
For certain people, they may do that. But for the vast majority of people, they will not.
1P does not enjoy the popularity that Facebook is at. In the western world, one can reasonably expect any random given person to have a Facebook profile. The same cannot be said for 1P.
In the US, it will probably get you denied entry, possibly permanently, for "lying to a customs officer" (if a non-citizen), or the device possibly being confiscated if you're a citizen, (and a note in a file somewhere that says you've probably lied to a federal agent — particularly if they happen to catch any security camera footage of you stupidly using your device shortly after exiting the international arrivals area).
