Enrolling students in a google groups mailing list automatically as a way around sending limits?

Related to this: Bulk emails sending too fast causing gmail to block account. Is there a way to rate limit?
The whole “only 2000 emails per day” gmail limit is definitely going to be a problem for me long term. Google groups can send to a much larger number of students per day (6.2 million per hour ;)). The problem is of course that I don’t want to manually have to sign up every student.

I know this is a long shot, but is there any way that if I have a google group set up, I can make it so that everyone who registers for a given class, also registers to be in the class google group? (The group would be set for 1 way communication. They would receive only, they couldn’t send to the group.)

Google Groups sometimes seem to have a “Direct Add” feature – I think maybe they’re trying to get rid of it, though, because when I search I see that some people who are stuck with the newer interface don’t have access to that feature.

I think generally it’s going to be a little tricky to find free mailing list options that allow direct-add/bulk-add, just because that’s very easy for spammers to abuse. (Personally, I’ve been pretty happy with groups.io, but you’d need to pay $20/month for the tier that includes direct-add—although you can also downgrade to free for months that you don’t need that feature, which is what I’ve done, heh.) And I don’t know which ones would have API access.

I suspect a better bet would be finding an email service that has a higher sending rate limit. Again speaking personally and not for my employer, I use Fastmail for my personal email as well as for sending a small number of service emails. I see that their limits are a good bit higher than 2000/day, but note the per-hour and per-10-minutes limits; I’m not sure how “bursty” Open edX’s bulk email sending is.