Thanks for the reply.
Yes, I'm sure the messages are going to the DreamHost trash folder. I can see them there using webmail and clear them using the webmail Purge feature.
I have the iPad settings as you describe, but the reason for wanting messages to be deleted from the server as well as the iPad is so those same deleted messages don't show up on other devices, in my wife's case an iPhone and MacBook.
I hear you about the similarity to the recycle bin, but if I'm sure I want to permanently delete something on my PC I can shift-del it and it's gone. Same thing with mail using a Windows mail client.
What would work, I'm thinking, is an option to delete Trashed messages after a period of time...a week, month, etc. That would give you time to catch a mistake if you make one but would still avoid the necessity of housekeeping using webmail.
If there's no such feature I'll post it on the suggestions forum (and not hold my breath).
edit: I have posted this request on the Suggestions board.