I know what you mean. As he got older, and after his stroke, Paddy used to come to be picked up often, usually when he wanted feeding, but again I think also it was the reassurance element. He'd sit in front of me until I picked him up and cuddled him, and spoke to him with the vibration thing. He hated being picked up until his stroke. Typical cat.
Towards the end, I think it was economy of movement for him - and why have staff and walk, when you can have a carry and save old achey bones?
I hope you can get Drum sorted, whatever you discover works for you both.