Why does VGA have so many ground pins (compared to DVI-I for example)?

First: What's critical isn't so much that there's a ground pin for each signal as much as that there's a ground pin near each color signal. The cross-shaped ground pin largely satisfies that requirement.

Second: DVI doesn't prioritize high-quality analog video -- it's a Digital Video Interface, after all. The small loss of quality incurred by using a single analog ground pin was probably considered acceptable by the designers.

The HD-15 (aka DE-15) connector for VGA connection was compatible with hand-crimping of pins to conductors of coaxial elements of the multiwire connecting cable. That practically requires a two-pin set for each of R, G, B video signals, to accommodate a signal pin and ground (coaxial shield) pin. Those signals were not logic level, and lacked the noise immunity conferred by the logic margin.

The DVI-I analog compatible signals may use the same wiring, but hand-assembling of crimp connections is no longer how the cables are constructed. As for the digital signals, in DVI-I and DVI-D cables those are twisted pair with shield, so require three wires each for up to seven fast digital signals. To my knowledge, there aren't any hand-assembly crimp pin options, the cable connectors are intended for machine wiring. In any case, twisted pair digital signals are noise-insensitive (because the digital signals have a significant logic margin). The shielding of those digital pairs prevents crosstalk, but the shields carry very small currents. Four pins (shaded yellow in the above question) are shared for up to 7 twisted-pair shields.

You are confusing the DVI connector with the cable. That "single" analog ground is a big honking ground, but what goes into a cable? The simplest is a DVI-A cable, which usually has a VGA connector on the other end. Internally, it will carry 3 color channels (red, green and blue) and 2 sync: vertical and horizontal. And guess what? A DVI-A cable will typically have 10 conductors. That is, 5 twisted pairs, 3 for color and 2 for sync, each with a ground line. The 3 analog color grounds will be connected to the cruciform analog ground on the DVI connector and the sync grounds will be connected to another pin.

So, just because a DVI analog section only appears to have a single ground, that does not mean that the cable does as well. In fact, the cable and the VGA connector will have the same number of ground pins (5) as a standard VGA.