This is the companion of D7031. That patch adds a new DIMENSIONS node to the depsgraph for each object that has geometry. However, this node is only necessary when there are drivers using an object's dimensions as variable. Since this is rare, it's easiest to remove these nodes after they turn out to be unnecessary. This is what (almost) happens in this patch.
Removing nodes from the depsgraph is hard, and there are no functions to do this yet. Instead, this patch recursively removes all the incoming relations from unused no-op nodes (i.e. no-op operation nodes without outgoing connections). Actually removing the nodes will be left as a future improvement.
I've tested this on a Spring file and it has no obvious performance impact on viewport playback.
Here are there results of blender --debug-depsgraph-time spring_02_055_A.eevee.blend and letting it run for a while to stabilise the reported FPS.
master: 11.7 FPS
Just D7031: 11.7 FPS
Just D7033: 11.8 FPS
Both D7031 + D7033: 12.3 FPS