Maybe they do not want to have new clients, which send out a lot of emails?
If you are on shared or (to a lesser extent) VPS hosting, then this is absolutely the reason. If you buy shared hosting, then you are sharing an IP address with potentially a dozen other websites, depending on the size of the package they are selling.
Email providers like Gmail and Outlook only care about the mail server IP, so they don't care if spam is coming from your domain or another domain on the same server, it's the IP address of your server that's going to go on the blacklist.
Saying "email providers blacklist senders who send a lot of email" makes absolutely no sense if you think about it, because if that was true then literally no forum on the entire internet could send a forum newsletter unless they paid for a 3rd party service. It does however make perfect sense if you think about it from a business standpoint. The hosts you're calling will have thought; "what can we tell this person that justifies our restrictions that they are unlikely to question?"
You're not going to ask the hosts for a source for their claim over the phone, as they could just say "well we can't read out a URL to you over the phone, can we?" and then you'd be stuck. They know you're forced to take them at their word.
If they had said "we restrict emails per hour to stop the damage any spammers can do, so that your email delivery isn't affected" then you could counter with "but I'm not a spammer, can't you just lift the restrictions for me?"
That's not to say that they're inherently
wrong for restricting the emails per hour, as shared hosts
do have a responsibility to protect the other customers on their account. My point is, however, that if you are serious enough about your forum that you want to send a newsletter, then you may wish to pay for the premium of a VPS without such restrictions.
All of that being said, I can see a world where they may be
technically correct, for instance if every site on every server was sending out a newsletter at the same time and a large amount of those newsletters were being flagged as spam, then you could sort-of-in-a-roundabout-way say that it was the volume of the emails that caused that provider to blacklist the server.
Personally though, I would never accept such restrictions and I would look into either sending my email via Amazon SES (which we @ DBTech do, in spite of having a dedicated server) or buying a better web hosting package.
Fillip