I think police should need a warrant to use facial recognition in many cases. I also feel that perhaps searches of electronic devices and online accounts need to strictly limit exactly what is searched for and disallow any evidence of any crimes not listed in the warrant from being used.
I don't think that is realistic or even remotely reasonable. You know, people recognise other people simply by eye-sight; police officers do the same. We can use binoculars to see further away and thus enhance our vision, or we can use an infra red camera to see thing at night - and record it, and so on. There is a continuum from using no technological aid at all to using automatic recognition technology, so where should the limit be set? I think we have to weigh up the benefits against the costs. There is always a risk that technology can be abused - but it is already being abused by criminals, and if the worry is about civil rights issues privacy etc, then that can be addressed with proper education of the police; it does actually work. Most police officers do want to do their job well and be proud of themselves.
As for requiring warrants for using this sort of low-level data gathering is just plain silly - it is simply unworkable.
The 4th amendment is supposed to make it hard to prosecute certain kinds of crime. In my opinion, the police really have no business going after crime that isn't reported to them anyway, except for a few exceptions like murder.
According to Wikipedia (https://en.wikipedia.org/wiki/Fourth_Amendment_to_the_United_States_Constitution):
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized
So, the amendment talks about the right to privacy and the right to go about their daily business without being stopped at random by the police. The purpose of this is quite clearly not to "sort of allow certain kinds of crime to take place more easily", as if that was in itself desirable. It is the clear duty of police to investigate crime - all crime - and prevent it if possible, even to the extent that they have a near monopoly on doing so in most countries. Suggesting that they must only react to crime if it is reported to them is blatantly absurd.