As a counter point, If you stop testing you inherently stop looking for variants as that's part of the test process. Your only sign that a new really bad variant kicks in is after hospitalisations/deaths spike past the "norm", which would then mean containment is impossible as community spread has already occurred.
While in the long run testing will have to stop, doing so right now would be undeniably a risky move. Vigilance is the sensible way to go here I feel. If we had all been more Vigilant at the start of this things would have been very different.
While direct action should only come from hospitalisations/deaths. monitoring at the moment is needed.