Why we study continuous time systems if in the real life we control them using micro-controller which is discrete time .. ?
A controller is built around a physical system. What is the open-loop behavior of the system?
You have to sample the physical (continuous-time!) system in order to provide feedback to your discrete controller. What sampling rate should you be using for that microcontroller? Are you sure?
Once you have the physical system modeled and the sampling mechanism designed, how do you develop the controller? Well, with Laplace transforms you could do PID control or state feedback control, but all of those use continuous time differentiators ($s$) or integrators ($1/s$).
So, how do you perform differentiation or integration in a discrete control system? Easy - the Z transform! But, which Z-transform? Do you use the Tustin Bilinear Z-transform? Well, that's great but it has some frequency warping. You could maybe avoid that by using a Z-transform that maps your poles correctly, or you could use a Z-transform that maps the impulse response, or you could do something more advanced.
Point being that, like all of engineering, there are trade-offs. Every method of converting a continuous time controller to a discrete time representation of that controller introduces unwanted aspects. It's up to you to understand the various drawbacks and apply the correct approach.
But, how can you understand a drawback unless you have a "perfect" system by which to compare all the others? This is a similar argument for studying ideal/frictionless systems in physics - you need to understand what the best possible outcome is in order to understand your limitations.
Nevermind the fact that you could also implement an analog controller.