Until you get to super-high-res textures and the like, the throughput isn't nearly as important as the latency.

At 200 MB/s the way hard drives usually measure it, you're able to read up to 390,625 512-byte blocks in 1 second, or to put it another way, a block that's immediately available under the head can be read in 2.56 microseconds. On the other hand, at 7200 RPM, it takes up to 8.33 milliseconds to wait for the platter to spin around and reach a random block on the same track. Even if these were the only constraints, sequentially arranging data you know you'll need to have available at the same time cuts latency by a factor of about 3000.

It's much harder to find precise information about the speed of the head arm, but it also usually takes several milliseconds to move from the innermost track to the outermost track or vice versa. In the worst case, this would double the random seek time, since the platter has to spin around again because the head wasn't in position yet. Also, since hard drives are so large nowadays, the file system allocators actually tend to avoid fragmentation upfront, leading to generally having few fragments for large files (YMMV).

So, the latency on a hard drive can be tolerable when optimized for.

> On the other hand, at 7200 RPM, it takes up to 138 microseconds to wait for the platter to spin around and reach a random block on the same track.

You did the math for 7200 rotations per second, not 7200 rotations per minute = 120 rotations per second.

In gaming terms, you get at most one or two disk reads per frame, which effectively means everything has to be carefully prefetched well in advance of being needed. Whereas on a decade-old SATA SSD you get at least dozens of random reads per frame.