CDPR did something nearly every RPG or Open world game does. They made the main quest have a time count down that overwhelms/looms of side quests.
Skyrim does it. Why am I helping this dude recover his friend's bodies from a cave if Alduin the World Eater has returned and I'm the only one that can stop him. Fallout 4, is go find your infant son. BOTW, wtf am I doing fucking about when Gannon is on the rise? RD2, Arthur is imminently dying from TB but yet here I am romping around with no problem at all as long as I ain't doing the main story.
V dying from the chip is just like that, it's a flaw that many of these games have. Few games try to fix it, FNV has it so that the main quest factions that drive the story could do with your help/freelancing to put them in the best position. Morrowind makes it so you need to ingratiate yourself among the houses so you can be in a powerful enough political situation to deal with Dagoth Ur. This encourages you to do side quests.