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This should fix the crashes in question, which deref |profile_| during
construction.  It also seems more obvious; it's not clear why we should avoid
providing the profile until Init().

This also does a lot of misc. cleanup, e.g. moving member inits into the
declaration.

Bug: 1033456
Change-Id: I44f57c90bb14da4ee116259340b7892a1db6802e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1965899Reviewed-by: Evan Stade <estade@chromium.org>
Commit-Queue: Peter Kasting <pkasting@chromium.org>
Auto-Submit: Peter Kasting <pkasting@chromium.org>
Cr-Commit-Position: refs/heads/master@{#724731}