Wow, that is a pretty extreme position. (I can't dismiss it outright as obviously the senate can debate things and come to conclusions and make policy, even if all the debates and hearings are public.)

In your opinion should politicians be allowed to meet each other and talk privately (about politics) at all? Or should there be no private meetings allowed? (Or at least no talking politics if they do meet.)

I would actually strongly disagree with that. Officials need to be able to exchange ideas freely amongst themselves and within confidence in a non-media environment. They need to be able to say things to each other in person, on phones, and in email communications in less discrete terms that otherwise would need to be crafted to appease their political coalitions and oppositions. They need to be able to ask and say stupid things. If you take that away from officials they lose their ability to actually deliberate and think about policy in terms of the merits of the policy. There is a balance to strike in terms of transparency and public accountability, but a transparency free for all in which no communication is private can easily lead to bad policy and outcomes.

Its not too different from not having a client see your business's internal communications. 99% of the time you aren't trying to screw your client and are trying to do a good job for them, but you really don't want to show them the sausage factory in any case because it will make it harder to do a good job for them if everything you do or say is presented to the client.

The impossible grey area would be what defines 'urgent.' Nevertheless, I would welcome less abuse of state secrets privilege.