This is going to require multiple steps. Started adding individual steps as blocking bugs.

After the 4 blocking bugs are fixed it should become possible to delete PaletteDelegate completely.

 Issue 647417  has been merged into this issue.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/b48c7f4242f23b60127bad17f6090d9d36df4068

commit b48c7f4242f23b60127bad17f6090d9d36df4068
Author: Vladislav Kaznacheev <kaznacheev@google.com>
Date: Mon Oct 16 19:13:46 2017

Delete PaletteDelegate

Now that all useful features have moved out of PaletteDelegate
it is time to delete it.

Bug:  761120 
Test: ash_unittests --gtest_filter=Palette*:Metalayer*
Change-Id: I65012c040f6722a0c05240a06f0b8084ef90e440
Reviewed-on: https://chromium-review.googlesource.com/721721
Reviewed-by: James Cook <jamescook@chromium.org>
Commit-Queue: Vladislav Kaznacheev <kaznacheev@chromium.org>
Cr-Commit-Position: refs/heads/master@{#509132}
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/BUILD.gn
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/mus/shell_delegate_mus.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/mus/shell_delegate_mus.h
[delete] https://crrev.com/b9e44824886e5f96cd8c0b3302c4225263614efc/ash/palette_delegate.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell/shell_delegate_impl.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell/shell_delegate_impl.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell_delegate.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell_test_api.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/shell_test_api.h
[delete] https://crrev.com/b9e44824886e5f96cd8c0b3302c4225263614efc/ash/system/palette/test_palette_delegate.cc
[delete] https://crrev.com/b9e44824886e5f96cd8c0b3302c4225263614efc/ash/system/palette/test_palette_delegate.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/system/palette/tools/laser_pointer_mode.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/system/palette/tools/magnifier_mode.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/system/palette/tools/metalayer_unittest.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/test_shell_delegate.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/ash/test_shell_delegate.h
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/chrome/browser/ui/BUILD.gn
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/chrome/browser/ui/ash/chrome_shell_delegate.cc
[modify] https://crrev.com/b48c7f4242f23b60127bad17f6090d9d36df4068/chrome/browser/ui/ash/chrome_shell_delegate.h
[delete] https://crrev.com/b9e44824886e5f96cd8c0b3302c4225263614efc/chrome/browser/ui/ash/palette_delegate_chromeos.cc
[delete] https://crrev.com/b9e44824886e5f96cd8c0b3302c4225263614efc/chrome/browser/ui/ash/palette_delegate_chromeos.h

PaletteDelegate has been broken down into feature-specific parts (notes, screenshots, stylus prefs, metalayer) and deleted. The only part that remains mash-incompatible is palette screenshot tools (Issue 557397)