Anyone who has ever made a tomato-based pasta sauce has probably noticed the thick, dark red trail the sauce leaves behind on the walls of the pot as it is reduced. This sticky residue is (free! bonus!) tomato paste, and it should not be abandoned under any circumstances.
One of the main reasons we simmer tomato sauce for so long is to drive out the water and concentrate the flavours, and by failing to incorporate the side paste into your sauce, you’re leaving that concentrated flavour behind, which I’m sure you do not want to do.
There’s an easy fix for this: Just scrape around the side of your pot as the sauce reduces, tapping that paste back into the simmering mass of tomatoes from whence it came. Pacing-wise, I like to do a paste check every 15 minutes or so; the paste will eventually dry out if you leave it on the side of the hot pot for too long, and that will make it hard to remove (and can make it taste burnt).
But even too-dry, stuck-on paste isn’t worthless. I’ve found that it can be wiped off quite easily with a chunk of stewed tomato. Just grab a big hunk of tomato with tongs and wipe it around the side of pot; the heat and moisture radiating off of it will steam the stubborn paste right off, ensuring no flavour is left behind. Toss the pasty tomato back into the sauce, let everything reduce some more, and repeat until you’ve reached your desired level of sauciness.