XRSettings.gameViewRenderMode does not change Game View Render Mode

Reproduction steps:
1. Open the attached project ("Set-VR-Game-View.zip")
2. Open "SampleScene" scene
3. Enter Play mode
4. Press F12 (Can be changed in "Toggle Game View Script" Game object)

Expected result: GameView Render Mode changes
Actual result: GameView Render Mode never changes

Reproducible with: HDRP 7.5.1, 8.2.0, 10.1.0 (2019.4.14f1, 2020.1.12f1, 2020.2.0b10, 2021.1.0a3)
Could not test with: 2018.4.28f1 (XR SDK not available)