The 4th Amendment doesn't just require "a warrant". The English government was using "writs of assistance", a type of general warrant that granted broad powers. As a protection against that type of easily-abused power, the founders created a set of requirements that limit the scope of allowed warrants.

    ... 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.

While a judge might deny some extremely bad requests for a warrant, the point isn't about a judge denying warrants or proving anything to anyone. That kind of legal arguing can happen later in an actual court. Instead, warrants - as allowed under the 4th Amendment - establish the limits of power.

The violation of personal rights is allowed, because of specific reason ("probable cause"), in a particular place, limited to specified people or things. These limitations slow down the application of power and (hypothetically) create opportunities to fight back when authority is exceeded.

> no-knock warrants

I suspect those are constitutional when the are properly targeted to a specific event/person/etc. The tactics used to implement the search isn't limited by the warrant.

> secret warrant

That's may be a problem, but it may depend on the specifics.

> what's really stopping them from getting a warrant

Generally nothing, but that's the wrong question. If police are making many requests for specific warrants, that's the warrant system working as intended.

However, playing word games to pretend wiretapping everybody isn't "seizing" data until an agent looks at it is exactly the type of general warrant that is banned by the 4th Amendment.