The training seems to have changed in this regard over the years....
I guess it also has to do with the environment you train in.
If you train at a school that mainly caters to pilots that eventually want to fly commercially, you'll see lots of emphasis on actually using a checklist. Because that's what you do in a B737.
On the other hand, if you train at a school that mainly caters to pilots that want to fly for fun, on very simple aircraft, you'll see more emphasis on working from memory.
The PA28 checklist I got when I trained for my PPL/SEP, at a school which provides mostly professional training, ran for two densely packed A4 pages. But I'm also training for my glider license and I have yet to see a written checklist there. Everything is done from memory.