More generally, this is actually an old idea that of the "tactical nuclear exchange" with a few nukes being perhaps exchanged in Eastern Europe without a full-scale war.

Yes, and I seen nothing particularly wrong about this idea -- it's a possibility.

The wrong aspect about this is that it seems very unlikely to actually stay that restricted. And it may not at all be easy for a country to tell that another launched only a few nukes and isn't intending to use more. The standard way this sort of thing goes wrong is where the exchanges get pushed farther East and West until they are close to Moscow and Paris and then all hell more or less breaks loose.

However I don't think the current Russian elite (with bank accounts in Switzerland, houses in the Cyprus, sending their kids to English private schools, etc. etc.) would be willing to contemplate high risk of even a limited nuclear exchange.

That seems likely to be true, but how much influence do they have? And note that even with Putin's repeated mentions of nukes they haven't taken any steps to curtail the situation. A nuclear exchange if it started could start well before they had a chance to do much about it.