Tire are the MOST important part for driving safety. Not even the driver can compensate for a lack of tire grip. Those 4 gooey contact patches are the only thing between you and death. Installation is important but doesn’t compare to the quality of tire. Not always, but generally you get what you pay for. $40 tires are junk, $250 tires will always perform better. Not neccessarily wear longer, but usually they do that, too.
Reduce the chance of getting in an accident? Yes, absolutely.