Do they really think it is that difficult to set up fake social media profiles? To scrub search history? This notion will be completely ineffective at stopping any criminal behavior. Anyone too stupid to get around this is too stupid to actually be a threat to anyone. Though it will cause another cottage industry to spring up - tech types of questionable morals providing a scrubbing service.
The pro disarmament types are just looking (literally) for excuses to say "no" to people. The added benefits (from a pro disarmament standpoint) will include:
*) Increased cost to purchasers of firearms, reducing the number of people in the market. (impacting certain demographics more, but they won't get called racist.)
*) Delays in firearms purchases as they obtain and review this information. You think the current background check system gets overloaded? Ha! I predict it would take weeks to get through this system.
*) The government (aka globalists) get access to even more of your personal information. Do you really think this search data and your name will be forgotten? It will be accumulated so that they know exactly who to target with their UN swat teams when the time comes.
They are not interested in stopping street criminals. Street criminals are no real threat to the Elites. YOU ARE.
Plus, they WANT you to try to get around this by scrubbing your search history, because when you do you will find that they criminalized any attempt to evade evaluation.