Are there vertical through-hole USB mini B plugs?
Is there any particular reason they don't seem to exist?

Yes. Behold: USB Mini-A and Mini-B have been deprecated since 2007
http://www.usb.org/developers/Deprecation_Announcement_052507.pdf

Dear USB Developer,
With the recent introduction of the Micro-USB connectors, the USB-IF is taking the strong step to
deprecate the Mini-A and Mini-AB connectors in order to minimize the number of cable combinations
required to support the various product interconnections and minimize marketplace confusion. Based
upon this, the USB-IF will no longer certify products that use the Mini-A and Mini-AB connectors nor
products that use them. This change is effective immediately. Vendors of USB On-The-Go (OTG)
products are directed to adopt the Micro-AB receptacle on all new OTG designs in lieu of the Mini-AB
previously approved for this application. In addition, all Mini-A and Mini-AB connectors that are currently
on the Integrators List will be removed.