Protocol handler should probably be deleted with site settings. 
They need to be added to the site settings counter and it needs to be checked if they support timestamp based deletion.

Note that external protocol handlers are currently deleted with cookies and site data (DATA_TYPE_EXTERNAL_PROTOCOL_DATA).

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/5decc53ab1b02778a8e05400efafd45424132a28

commit 5decc53ab1b02778a8e05400efafd45424132a28
Author: Christian Dullweber <dullweber@chromium.org>
Date: Thu May 03 14:53:13 2018

Delete protocol handlers with site settings

Protocol handler are site settings and should be deleted when a user
decides to remove site settings from Clear Browsing Data.
In order to allow precise deletions, we need to add a timestamp.
Old handlers don't have timestamps, so they are treated as created at
base::Time(0) and will only be removed if all data is deleted.
Preinstalled and policy defined handlers are not removed.

Bug:  824131 
Change-Id: I2599a53ff5712d5aac28ba4024bb0bc123aa32e6
Reviewed-on: https://chromium-review.googlesource.com/1000697
Commit-Queue: Christian Dullweber <dullweber@chromium.org>
Reviewed-by: Matt Giuca <mgiuca@chromium.org>
Reviewed-by: Martin Šrámek <msramek@chromium.org>
Cr-Commit-Position: refs/heads/master@{#555726}
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/BUILD.gn
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/chrome_browsing_data_remover_delegate.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/chrome_browsing_data_remover_delegate_unittest.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/counters/browsing_data_counter_factory.cc
[rename] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/counters/site_settings_counter.cc
[rename] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/counters/site_settings_counter.h
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/browsing_data/counters/site_settings_counter_unittest.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/custom_handlers/protocol_handler_registry.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/custom_handlers/protocol_handler_registry.h
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/browser/custom_handlers/protocol_handler_registry_unittest.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/common/custom_handlers/protocol_handler.cc
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/chrome/common/custom_handlers/protocol_handler.h
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/components/browsing_data/content/BUILD.gn
[modify] https://crrev.com/5decc53ab1b02778a8e05400efafd45424132a28/components/browsing_data/core/counters/browsing_data_counter.h