Well, algebra is a language created with the goal of making simple things easy to communicate. Yes, I'm getting in a tangent and calling operations in an infinite and non-countable basis "simple", but just try to do anything complex in non-linear algebra and it all falls apart already, never mind completely discontinuous functions.
Category theory is a language created to communicate complex models. If it's not obvious yet that you can't use CT the same way you use algebra, let me state so: you can't. CT must be less powerful than algebra, because you can't reason about complex stuff as easily as you can reason about simple stuff.
Yet, one mostly can not write a program nowadays without using CT. There's no language that does not implement a subset of it. You don't notice it for the same reason that fish do not notice the water.
But as powerless as CT must be, it gives you plenty of tools for simplifying your models, and not having those tools available can only make your program more complex, never simpler.
Category theory is a language created to communicate complex models. If it's not obvious yet that you can't use CT the same way you use algebra, let me state so: you can't. CT must be less powerful than algebra, because you can't reason about complex stuff as easily as you can reason about simple stuff.
Yet, one mostly can not write a program nowadays without using CT. There's no language that does not implement a subset of it. You don't notice it for the same reason that fish do not notice the water.
But as powerless as CT must be, it gives you plenty of tools for simplifying your models, and not having those tools available can only make your program more complex, never simpler.