While solving the Hamiltonian, books concentrate on the horizontal flow with only one mass attached to the string. Isn't there any consequences if we add more masses and why is friction always ignored?
Isn't there any consequences if we add more masses
Yes, there are indeed consequences. Typically you need to decompose the system into normal modes of oscillation.
and why is friction always ignored?
It's always ignored except in the places where it is not ignored, where we typically use the term damped harmonic oscillator.
(Within quantum mechanics, on the other hand, friction is a rather complicated thing - you can indeed do it, but it requires an open-systems approach and dealing with mixed states instead of pure states. Again, perfectly doable, but certainly not within the confines of a standard undergraduate course in QM.)
If you've only read introductory material, then you've only seen a skewed perspective on the total of things that are done, with a strong bias towards simplicity. If you want to free yourself of that bias and see what happens if you do add friction or more masses, the terms in italics above make good search keywords to get you started.