Some of our junior school teachers send emails to parents at the end of the week to say a pupil has done a really good piece of work. Sometimes they forget to note who they've sent it to and want to check before they keep sending the same thing to the same parents each week. They don't have access to the Email logging in the Control Panel, but wading through myself there were over 5700 emails sent between last Friday and now, and that is not searchable.
Create a "My Sent Email" module of its own (thinking HR might find it useful too) which would be effectively Sent Items from a normal email account. This should be searchable by subject, recipient and sent date. Attachments should be viewable.
Permissions should be read only with no options for Write, Modify or Full Control so that people cannot delete emails that might be needed for a subject access request.
The ability to "reply" to the email to pick up somehting a parent has not responded to would also be useful.
While I agree that it could be a useful feature to be be able to see what you have sent within iSAMS, it should be noted that if the teachers are using the Email Wizard in Student/Pupil Manager, then the default setting is to log the message in the pupil's Communication History, so giving the teaching staff read access to that 'view'in Pupil Manager would help them see what they have sent to a particular pupil.
For an alternative approach, I created a custom SSRS report to do [some of] what you want. It only allows searching between two dates (not by subject or recipient) and viewing the message text (not prettily formatted, nor any attachments) but could serve as the basis for a project to create a more fully-featured version. Let me know if you would like a copy of my RDL (bwray AT tudorhallschool DOT com).