Thin wires work perfectly well with screw terminals, you just need to follow the right guidelines.
Just one turn under the screw, so that the wire does not cross itself. If it crosses, when tightened, it will scissor itself and leave a weak point.
The wire must be supported before it goes away from whatever the terminal is fixed to.
If the wire is unsupported, it will flex, flexing solid wire will break. This applies equally to wires soldered to a board. Any adhesive that dries with a bit of give works well. Any line joint (wire to wire, wire to tag) will need support - heat shrink does a good job of not only insulating the join but making a strain relief each side.