Welcome to the Quilting Board!
I'm a firm believer that if it works, don't fix it. I was taught to square up with 2 rulers and not use the mat so that is how I am use to doing it. But if you have done it your way for a long time and it works, keep doing it.
I used the lines on the mat exclusively for years, ad my poor mats are showing the wear, so I have started using the mat lines when I need to make a very long cut, or a cut something wider than my widest ruler, but otherwise use the ruler lines and cut across my mat at odd angles to avoid the "ruts". I haven't found any problems with cutting discrepancies so far, but my current project is very forgiving so problems may show up in future, more precise, piecing that aren't an issue now.
If its an even inch measurement, and it doesn't have to be really precise, then I use the mat. But if its something like 2 3/4", I can't visualize that adjustment on the mat every time and use the ruler, so mostly I use the ruler. But, hey, if you're not having any accuracy problems, then do what works !
IMHO that's what those lines are there for. I use them.
I totally agree with Feline Fanatic. If you always use your mat you might well have a groove distortion from cutting in the same place a lot of times. I'm not willing to buy mats that often. With my ruler I can start and stop where I choose and in increments I choose.
Have fun quilting! If it isn't fun, you will miss a lot.
I rarely use the lines on the mat at all. And just the thought of lining the fabric up on the mat lines AND then lining up the ruler with the mat lines boggles my mind. Seems like too much! I have been quilting for over years and have satisfactory results just using the ruler.
But use whatever method works for you.
I use the mat to square up fabric and I've also run my rulers and measuring tape along the lines to see if the measurements are the same and I've seen no difference.
Perhaps the weight of the ruler on the fabric makes the ruler "more accurate", but I wonder - if all these matt manufacturers were not accurate, how could they stay in business???