This was a brilliant design. It had to balance cost in terms of pins and dynamic refresh, with capacity and reliability.

It hit a sweet spot for everything that basically let this design take over the world of early computing and it was easily composable to larger memory sizes up to a point that was sufficient for the time.

There's a pretty good reason this style of RAM is used on so many machines of the time, in pretty much the same configuration, and that you can pretty much swap RAM chips between machines of this time.

We are at an interesting point in computer history IMO. Microcontrollers are getting fast enough to keep up with most things happening inside the first (or first few) generations of personal computers. Before, you had to use FPGAs. Now, people use the Pico to create things like digital RGB upscalers or N64 cartridges. The Raspberry Pi Pico is fast enough (or almost fast enough) to keep up with most timing transitions of the 4116 and/or 4164, and I was able to create a Raspberry Pi Pico-based RAM tester that tests 4116 or 4164 RAM chips _live_ as they are being driven by an MSX. If you're interested, take a look at my blog entry here:
The amazing thing (as Ken points out right at the end) is the latest chips store 16 gigabits, about a million times larger, in a similar area. So you can think of each of those 1979 transistors as now containing 10^6 2020's transistors! It's mind-boggling. Also a million transistors is approximately an Intel 80386 (actually it's a little bit more).
Neat! I remember feeling very, very fancy when I got my Timex/Sinclair 16K RAM pack. It used 4116 chips. I was puzzled why they'd have so many chips in the expansion instead of just using static RAM, but back then everything was pricey. Compared with the 2K of RAM the TS/1000 comes with, this was a huge amount of memory :)
Always interesting how much engineering went into a 'simple' early chip like this. This was state-of-the-art once. :-)

Never liked these 4116s myself due to their multi-supply voltages. Common cause of problems where used (like in the ZX Spectrum as another poster pointed out).

And of course Ken Shirriff is brilliant as always!