Can a ground wire be too big?

A ground wire cannot be too big in any safety sense. The NEC sets minimums, not maximums, and a fatter ground clears faults faster and drops less voltage while doing it.

The practical ceilings are mundane: lug and terminal ranges only accept certain sizes, big copper costs money, and stiff wire is miserable in small boxes. An oversized ground that does not fit the terminal is its own violation.

Sometimes oversizing is mandatory: upsize the circuit conductors for voltage drop and 250.122(B) scales the ground up proportionally.

Mixing sizes the other way is the real hazard; a #10 ground protecting a circuit that Table 250.122 says needs #6 will run hot during the fault it exists for.

The ground sizing calculator gives the minimum and flags when proportional upsizing applies.