Hi Drew had similar issue client is buying these Google services but for some Google crawlers the from header was empty.
https://support.google.com/webmasters/thread/110658424/adsbot-google-does-not-include-from-googlebot-at-googlebot-com-header?hl=en
This was of course spoiling the WAF logs with false alerts so what we did is to strip the empty header with Irule when it comes in (bit nasty)
The another thing that should be improved is to mark this BOT as trusted as by default it is untrusted and you cannot overwrite that according to F5 support. So I agree with you this should be improved cause when you acquire their services it should be marked as trusted in my opinion.