I have been hopeful that the Whitney Hikers Association might be able to back a project to install a remote-reporting weather station at the summit hut. I went so far as to email a Seki ranger, who sounded positive, and gave me the name of someone to contact.
So I followed this lead, talking to several people within Sequoia National Park, and finally got to the Seki wilderness coordinator. We spoke on the phone for some time.
Here are the two big roadblocks:
The summit hut is protected as a registered property by the Natural History Preservation Act (of California, I believe), and a State History Preservation Officer would need to allow any modifications made to the building. I was told the building's original purpose was to "measure solar radiation", and that was done only for a single season.
The Mount Whitney summit is in a designated wilderness area, and introducing any kind of man made structures in the zone would practically require an act of Congress.
The person I spoke to also brought up the "slippery slope" point, that is, if you allow one group to bypass the rules, you will have dozens of other people coming with proposals.
I can think of a number of safety-related and scientific reasons that a weather station at the summit would be invaluable. And it would seem a weather station could be placed inside the building with only three externally visible items: anemometer, antenna and solar panel.
I haven't completely given up the idea, but don't hold your breath.