I do that too. I tend to "park" my cursor near where I am looking, or near where I anticipate clicking next.
> let's say that I want to login. My pointer is far away from the login link. My fingers are not on the touchpad. Is it faster to move my right hand towards myself, touch the touchpad, slide the pointer to the link or moving that very same index finger to the link and touch it?
Entirely depends on your relative proficiencies and preferences, I suppose.
When I had a touchscreen, I used it with a trackpad and a trackball. All three input devices had utility to me, so why not? These days I sometimes use a laser mouse rather than trackball, but same story (though my MacBook doesn't have touch now). I always prefer trackpad to scroll wheel for scrolling, for hopefully obvious reasons (range of motion and precision are both way better). I do know I got use out of the touchscreen even though I can't think of a hard rule for it. It's probably just nice to have on a case-by-case basis.
Personally I would not use the touchscreen very often, but I would use it sometimes to press buttons and maybe even to scroll. Maybe the resize handle in the bottom right corner of the text area I am writing now is a large enough target for a finger. On a laptop: raise a finger, drag and go back to the keys? Probably. With a desktop computer with a keyboard far away from the screen? Well, the mouse is also far away from the hands so who knows.
I never have a real use case for a mouse but sometimes I follow a link from HN to a game in which a mouse would be better than a touchpad: move move move click click move click is great with a mouse and terrible with touchpad of all kinds. My mouse is in a drawer somewhere.
I am a fan of touchpads with physical buttons. I think that only HP is selling them anymore, on very few ZBook models (maybe a 16 Fury?) and Lenovo still has them in laptops with their stick in the middle of the keyboard. However the Lenovo buttons are at the top of the touchpad, where the thumb rests if the index finger operates the stick. The thumb rests below the touchpad when operating the touchpad.
Thinkpad fans will tell me that those buttons are close to the space bar, were thumbs rest all the time and they are right. Their little stick is very conveniently placed but I never manager to operate it as efficiently as a touchpad, which required zero training. My old ZBook has both the stick and the touchpad and two rows of 3 buttons, and I've never learned to move the pointer with the stick, both Windows and Linux.