I came here looking for another answer, but let me see if I can help some of you. A decade or two ago, you could easily add dozens of emails to outgoing emails. Unfortunately, in the current digital age, email spamming is just too rampant that email providers like Google and many others have had to provide a way to curtail that. So by doing that, yes, it's made it a little difficult to just send out a bulk email to a lot of people that actually DO need to receive your email.
So with that said...what most of you are describing actually fits well within the confines of an email marketing program like Mailchimp. They have a free version that (at the time of this writing) includes up to 2,000 contacts and 10,000 monthly emails, which is pretty generous. My business, Promofuse Solutions, sets this up for a ton of clients using the free version. It may seem complex when you first look at it, but really, once your contacts are imported in, sending out emails is really pretty simple. We usually set it up for a small fee, and then walk the customer through how to use it so that there are no recurring costs. We have never really had a problem with them being able to use it once they've had the walkthrough.
I'm not affiliated with Mailchimp in any way, but I appreciate software that makes certain tasks easy without requiring another monthly subscription for basic level service. I hope it helps some of you achieve what you were trying to do. Feel free to look us up if you need any help setting it up.