> Almost no day-to-day policing is done with warrants!

By this logic, there is no need for "day-to-day policing" to have warrants for:

  - phone taps
  - SMS messages
  - GPS history
  - email
  - banking information
  - justified arrests
  - court approved searches

The result of the position you advocate is known as a Police State[0].

0 - https://en.wikipedia.org/wiki/Police_state