I don't believe the datetimeformat is supported in email templates. My guess is that the filter isn't working correctly, leading to a malformed URL, which Google then defaults to the current day. I know the team would like to support these filters for email templates, but I don't currently have any timeframe on that.
That's a good question; supporting HubL filters on object tokens wouldn't necessarily mean that HubDB data would be supported. I would imagine that those would be separate concersns, and likely wouldn't be part of the same change unless that change is a major overhaul of sorts.
Happy to pass that feedback along as well; as I mentioned before, I'd also encourge you to post these ideas to the Ideas Forum, which is the best place to draw support for your feedback/ideas among the broader HubSpot community.