Joy
(@joyously)
Your web server, where your site is hosted, is built for serving web pages. It can send email, but it is not configured to optimize that. However, there are servers that are. These are usually called autoresponders, because a user can initiate a sequence of automatic emails, in addition to the owner being able to send broadcast emails at any time. These are better for email than your web host, because they handle bounces, blacklists, blocked domains, quotas, throttling, opt-in, double opt-in, the CAN Spam rules, lists, moving people from list to list based on clicks, tracking open rates, A/B testing, and setup of automatic sequence of emails for new subscribers.
It is very easy to get your server on a blacklist by sending too many emails. It makes so much more sense to use a service that is set up to handle all that for you. There are several free ones, too.
You will need an email solution that allows access to additional users (like assistants) with sending rights.
However, it is hard to imagine that any email service will disallow the user (or assistant) from viewing the subscriber list.