The whole point of Laplace is to make problems easier to solve by mapping linear differential equations to algebraic equations. To quote my dynamical systems pr

The whole point of Laplace is to make problems easier to solve by mapping linear differential equations to algebraic equations. To quote my dynamical systems professor, "you learned how to solve this in high school." There is a bit of hand holding in engineering courses with it however. A lot of looking at transform tables, and maybe a few problems where you need to exploit the properties of the transform or remember its definition to solve a problem. That can trip people up, and it happens in the real world more often than you'd like.