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It's one of only two remaining consumers of the SpawnedTestServer in
HTTP mode.  While the still need the SpawnedTestServer for some special
cases (e.g., client certs), it's no longer needed in any simple HTTP
case, and it's been an unending source of test flake.  Finally being
able to remove HTTP support from it is a big step towards deprecating
it.

Bug: 492672
Change-Id: If8fb9994d675950b0bbd718d4933da4925f0f64d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2510372Reviewed-by: Daniel Rubery <drubery@chromium.org>
Commit-Queue: Matt Menke <mmenke@chromium.org>
Cr-Commit-Position: refs/heads/master@{#822839}