Yeah, your instincts are correct!

There are at least a couple of Snowcovered modules that extend the functionality and control over the native Newsletter item, including the ability to do what you want. I really think the Admin/Newsletter menu item should have been called "bulk email" instead, since it is somewhat narrow in scope (no offense intended).

Some reasons to stray to something else (DataSprings, etc.) is that they offer so much more if you have the need - categorized newsletters, opt-in/opt-out, simple or advanced subscription capabilities, newsletter archiving and viewing, etc.  - to name a few.

FYI, in the next release of DNN core (end of 1st quarter or so?), the Admin menu items are reworked and handled differently whereby you can have full control over access similar to any other page or module on a DNN site. There were some recent blog postings that showed screen shots and descriptions.