The only understandable reason to use it as an excuse is if they're unfamiliar or uncertain of how to provide services or instructions or clearances outside of radar coverage. Otherwise they're acting in bad faith. I'm not sure which is more likely, probably the former if anything I'd hope.

I don't see ground movement or clearance delivery as something one would typically refer to as "non radar" though. Non radar to me describes things involving airborne or soon to be airborne aircraft without radar service. The glossary in the 7110.65 seems to agree. One doesn't even need to use top down mode to issue taxi instructions so its hard to see it as an excuse to not do top down tower cab service at least prior to departure even if somehow the people in question were unaware they had that feature in vERAM.

Radar coverage below certain altitudes is the thing that strikes me as most likely to be what they're referring to. I'm not sure what else they could mean.

is this still a thing?

Essentially, the pilot doesn't even have to readback the squawk code. Technically he could just say "Roger, N123AB," and that would be perfectly acceptable readback.

I just have a question: is the Cessna lifting the 747 and the Shuttle, or is it just attached underneath like on a dirigible?