Speeds do go up with density. Take an empty 4 TB drive and an empty 16 TB drive, and then write and read 2 TB of data to both of them. Since the platters on the 16 TB one are that much denser, you go over a lot more blocks in a single spin than the 4 TB one.
The 16 TB drive won't be anywhere close to 4x faster than the 4 TB drive, though. Maybe 20% (~200 MB/s vs ~230-250 MB/s). That's because most of the capacity increase comes from more tracks and more platters, not linear density, which determines throughput.
I would say 250-260MB/s for a 16TB drive, and when 4TB drives were newer they were more like 160-180MB/s. That's about a 50% increase.
Doing the math, you're probably going from 5 to 8-9 platters, so 2.2-2.5 areal density, and a naive square root suggests it should be about 50% faster. So maybe track width is taking a fair share after all?
Though when I look at more sizes, it seems like 12TB drives were also hitting 260MB/s and speed has almost entirely stalled since, with 24TB being only a hair faster.
That's a very logical theory, but it doesn't really seem to hold up in real-world data transfer speeds.
For instance: 7200 RPM SATA drives have been stuck in the peak-performance realm of between about 250 and 300 megabytes per second for a decade, even though maximum capacity has more than tripled over that time.
