The way the messaging system is constructed now is IMO a real security nightmare. It says, basically:
"A new message or response with subject:
has arrived for you to view.
Follow this link to view it:
We're trying on the 1 hand to discourage users from clicking links, & on the other hand we're forcing them to do it in order to view a legitimate message or forcing them to not get the message if they don't choose to click.
The entire message, I think, should be included in the message body, minus any sensitive information, of course.
I think the message also needs to contain more of an introduction, ie,
"this is a message from (provider's name) your hosting provider. If you desire, you may go to your control panel to view it, or read below. Something to more clearly identify the sender as their hosting provider & to give them an opportunity to read the message without clicking links, for corn sakes.
You can modify messages as you wish, just copy needed template like message_user.txt from /usr/local/directadmin/data/templates/ to /usr/local/directadmin/data/templates/custom/ and modify it as you want.