Sorry, I don’t know of any menu command that will do that, but it could be scripted, perhaps.
Not sure if you’re really using assignments or if you mean InCopy stories. Both appear in the Assignments panel. You don’t check out an assignment, you check out the InCopy stories. (But if you select an assignment name in the panel, and choose Checkout, that’s a shortcut to check out all the stories you’ve grouped into that assignment. Maybe that’s where you’re getting the idea.)
FWIW it’s usually not necessary to create assignments, just export all the stories to InCopy from the Edit > InCopy > Export All Stories command, and then all the InCopy stories appear in the Assignment panel in Unassigned Stories. Some people call those linked InCopy stories “assignments” too. Much confusion here because the name of the dang panel is Assignments. It’d be like calling the Paragraph Styles panel “Style Groups.” The Assignments panel should be called “InCopy Assets” or similar.
okay, end of rant. ;-D
Anyway, bottom line is you have InCopy stories in your Assignments panel. what might be a little bit faster would be to Shift-Click each assignment in the panel so they’re all selected, then click the Check Out icon at the bottom of the panel. That checks out all the stories. Do that for each file.
You might try asking if anyone could script this for you in the Adobe Scripting Forum
https://forums.adobe.com/community/indesign/indesign_scripting
AM