Exchange's New-MailboxExportRequest behaves strangely with DateTime parameters to ContentFilter
Solution 1:
I confirm I have solved this by specifying the content filter exactly as "(Received -ge '$startDate') -and (Received -lt '$endDate')" to prevent it from becoming $null with help from this question.
My client's Exchange Server 2013 version/build no. is 15.0.847.32.
It could be a rare condition, still I added my answer here just in case it helps someone.
Edit: Based on the concept, I have written a PowerShell Script to archive Journal Mailbox monthly with email reporting.