I think it's a bug with instance creation. Notice in the images I've uploaded how there are three green boxes for "Build Agent", "ServiceNow Studio", and "App engine studio" and in the image they're all shown as installed. If the instance is created with ServiceNow Studio installed then importing an app from source works. I believe this is controlled by checking the "Developer" box in the "My profile and settings" screen under your developer.servicenow.com account (see second screenshot).

Previously, in addition to having "Developer" checked, I also had "Other" checked with a role. When that was checked, even though "Developer" was also checked, ServiceNow Studio did not show as installed when the instance was created. Interestingly, I could actually run ServiceNow Studio in the instance, but importing via source control was not enabled. The Metadata Source Control plugin was installed and active, but source control import simply didn't work.

Deleting the instance, unchecking "Other" and then creating a new instance caused the new instance to come up with ServiceNow Studio installed and it functions correctly.

I think if Developer is checked the instance creation process should install ServiceNow Studio regardless of whether the "Other" box is checked or not.