I do, but it's mostly out of habit cuz it's usually the strongest one in my team by the time I'm done with the first route. Plus, the starters are usually pretty good for casual playthroughs.
Honestly, I have always kept my starter till the end on all games I have played. Even when I move on to do something else in the game I still use it every now and then.
I always keep my starters on my team till I get my dream team for that region.
An example of this is in Pokemon sword when I picked scorbunny but boxed him after my champion fight because I got a G-Max Charzaird.