A useful distinction
A puzzle with unlimited moves and no restrictions differs from one with a small move budget. Constraints shape the search for a solution. Adding a limit merely to make the screen look complicated can obscure the intended challenge.
Put it into practice
Try one paper puzzle with and without a chosen restriction. Record which decisions changed and whether the goal remained understandable. Test the actual combination of rules rather than assuming that an extra timer or blocked square automatically creates a better puzzle.