Remove non-deterministic tests

[elharo]

Description

Fixes #23119

Motivation and Context

These tests are fundamentally timing dependent and non-deterministic.

Impact

none

Test Plan

CI

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Release Notes

== NO RELEASE NOTE ==

[tdcmeehan]

#19675 fixes this by removing the non-determinism, let me see if I can get that done soon. Although this test is dependent on the environment, which we know can lead to flakiness, I don't want to delete it outright because the thing it tests is important.