The main ground strap from the battery runs to the engine block, where it can most effectively help complete the starter motor's electrical circuit.

But from there, the rest of the car needs to be grounded as well. Without an explicit wire leading from the engine to the car body, the current is free to find other more 'interesting' paths. Through the radiator shell, into the coolant, and into the block (causes galvanic corrosion). Perhaps through the drivetrain somehow, through several sets of bearings along the way, which could damage the finish and lead to premature wear. Some cars will have a secondary ground strap from the battery to the car for this as well.

In addition, the fuel injected cars have a lot of sensors in the head, sensors which often ground a signal wire to the head to send a signal back to the ECU. In an electrical sense, grounded is grounded, but in an electronic sense, there is a difference in quality between a 'somewhat' grounded object, and something grounded better, or worse, or from further away. Basically, there can be differences in current potential between what the sensor grounds the signal wire to and what the ECu is comparing the grounded signal wire to back in the footwell. I.e. noise in the wire, creating a noisy signal in whatever it's trying to sense (like coolant temp). Which leads to less effective ECU decisions being made.
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'63 PV544 rat rod, '93 Classic #1141 245 (now w/16V turbo)