[3.12] gh-124309: Revert eager task factory fix to prevent breaking downstream (GH...

[3.12] gh-124309: Revert eager task factory fix to prevent breaking downstream (GH-124810) (#124817)

gh-124309: Revert eager task factory fix to prevent breaking downstream (GH-124810)

* Revert "GH-124639: add back loop param to staggered_race (GH-124700)"

This reverts commit e0a41a5dd12cb6e9277b05abebac5c70be684dd7.

* Revert "gh-124309: Modernize the `staggered_race` implementation to support eager task factories (GH-124390)"

This reverts commit de929f353c413459834a2a37b2d9b0240673d874.
(cherry picked from commit 133e929a791d209b578b4822a7a07f4570b3803b)

Co-authored-by: Peter Bierma <zintensitydev@gmail.com>