Yeah, you covered this in your last line, but it's worth restating: you can put restrictions on the sale. Restrictions will, inherently, lower the value (since it will limit the licensing) but you CAN do it.
And bear in mind that it's not necessarily true that Dee Snider controls ALL of his publishing; The Beatles, famously, when they started "Northern Songs", thought they controlled their songs, but Dick James owned 50%, Lennon had 20%, McCartney had 20% and Brian Epstein had 10%. Later, the company went public (shares in the company were sold on the market) and Lennon and McCartney's take dropped to I think 15%. In 1969, Dick James sold his piece to ATV (not telling either Lennon or McCartney, even though James knew they wanted to control their music) and as a result, Lennon and McCartney sold out their shares.
Later, famously, McCartney told Michael Jackson the story - in the hopes of teaching Michael to keep control of his own music - and MJ went out and bought ATV!
There are also deals where the writers can still get residuals even if they don't own the songs anymore. Supposedly, there was no rift between McCartney and Jackson at the sale; but McCartney tried to get "a raise" as he called it, asking for more under the original deal that put the songs there in the first place. Jackson said no.
For me, I'd love to ask a Dee Snider what the intent was. It's basically an annuity, and there are pros and cons to selling that out. I can imagine Dee seeing the checks getting smaller and smaller each year, and deciding to cut his losses. RHCP? Who knows. But Dylan? That's a fucking gold mine, I would think. Blackmore has "joked" multiple times that Smoke On The Water has basically paid for his entire post-Deep Purple career (I've read interviews with Dio, Powell and Bonnet that seemed to indicate that Ritchie funded all of Rainbow, and recouped later on the touring and album sales. I imagine he's doing something similar with Blackmore's Night.)