Car width isn’t a problem. From 1978 until 1992, the cars were wider than they are now yet the cars could race less than a car length apart for an entire lap. The issue is the length, weight, and downforce. Overtaking issues are directly correlated to those three factors. That’s why on-track action continued to fall throughout the 90s as the cars got narrower; the aero got too complex, the cars became heavier and longer which made them less agile.
Excess length means you have to commit to a line earlier (meaning you can’t be as bold under braking), excess weight means the cars are less agile (meaning you can’t be as aggressive on corner entry), and excess downforce means dirty air makes the cars too unstable at speed when they’re too close. Creating the unholy trifecta of cars that can’t follow closely, can’t adjust their line in a corner, or be aggressive with each other.
Width is probably the least important factor. If anything, a wider car is EASIER to overtake with because it’s more stable meaning you can push harder both on the throttle and on the brakes.