Tim, I don't agree with you.
If I use an Exchange Server or other Mail Server softwares that support EAS (I have experience of a few, like MailEnable, mDaemon and Kerio), if I delete a mail in my smartphone with EAS, it is suddenly (within few minutes at least) deleted in the server too, ad so in IMAP and WebMail (assuming of course that the smartphone has active Internet connectivity).
If it does not work like that it seems to me a bug (or at least a malfunction in the specific installation)
Gabriele Maoret - Head of SysAdmins at SERSIS
Currently manages 6 SmarterMail installations (1 in the cloud for SERSIS which provides services to a few hundred third-party email domains + 5 on-premise for customers who prefer to have their mail server in-house)