But still DRAM is what you would use for a "real" system. Wozniak's design for the Apple II used a clever hack where the system actually runs at 2 MHz with an effective CPU rate of 1 MHz. Any read from a DRAM row will refresh the entire row. Approximately every other cycle the video system steps incrementally through memory, refreshing as it goes.
This is more about saving chips than saving cycles, since the Apple II was implemented entirely with 74 series logic. A more traditional approach that used spare cycles during horizontal blanking would have required several more chips.
It does mean that the layout of the Apple II's screen memory is somewhat insane. Those DRAM chips needed to be refreshed every 2ms, and it takes 16ms to scan out a whole screen. Every 8th of the screen needs to be spread out across all 128 rows.
The reason is that the designers saved a few chips by repurposing the Z80's refresh circuit as a counter/address generator, when generating the video signal. Specifically, it uses the instruction fetch cycle to read the character code from RAM, then it uses the refresh cycle to read the actual line of character data from the ROM. The ZX80 nominally clocks the Z80 at 3.25MHz, but a machine cycle is four clocks (two for fetch, two for refresh), so it's effectively the same speed as a 0.8125 MHz 6502.
I wrote a long section here about how the ZX80 uses the CPU to generate the screen and the extra logic that involves, but it was getting too long :) The ZX81 is basically just a cost-reduced ZX80 where all the discrete logic chips are moved into one semi-custom chip.
Doing this makes external RAM packs more expensive too. You couldn't use the real refresh address coming from the Z80 because the video generator would be hopping around a small range of addresses in the ROM, rather than covering the whole of RAM (or at least each row of the DRAM). The designer has two options:
1. Use static RAM in the external RAM pack, making it substantially more expensive for the RAM itself; 2. Use DRAM in the external RAM pack, and add extra refresh circuitry to refresh the DRAM when the main computer is using the refresh cycle doing its video madness.
I think most RAM packs did the second option.
The BBC Micro range all had 250 ns DRAM, with the CPU getting 2e6 accesses and the video getting the other 2e6 (taking advantage of the 6502's predictable RAM access rate). The display memory fetches served to refresh the RAM.
I don't know much about the Acorn Electron, which was very different internally, but it had dynamic RAM as well. I expect the video refresh was used to refresh the DRAM in this case too - as the display memory layout was the same, and so over every 640 microsec it would touch every possible address LSB.
The 6502 second processor had DRAM as well, refreshed by a circuit that ran on a timer and stole the occasional cycle from the CPU at some rate.
Though static RAM was quite common for RAM upgrade boards (of one kind or another), presumably cheaper for this case than the alternative.
For higher memory capacities, e.g. 32 kB, 48 kB or 64 kB, static RAM would have been too expensive and too big, even if 6502 did not have an integrated DRAM controller, like Zilog Z80.
Using SRAM instead of DRAM meant using 4 times more IC packages, e.g, 32 packages instead of 8. The additional DRAM controller required by DRAM would have needed only 1 to 4 additional IC packages. Frequently the display controller could be used to also ensure DRAM refresh.
The Apple II was one of the first 6502 systems to use DRAM (in 1977) and Woz was incredibly clever in getting the refresh for free as a side effect of the video generation
Static RAM (SRAM) is a circuit that retains its data as long as the power is supplied to it. Dynamic RAM (DRAM) must be refreshed frequently. It's basically a large array of tiny capacitors which leak their stored charge through imperfect transistor switches, so a charged capacitor must be regularly recharged. You would think that you would need to read the bit and rewrite its value in a second cycle, but it turns out that reading the value is itself a destructive operation and requires the chip to internally recharge the capacitors.
Further, the chip is organised in rows and columns - generally there are the same number of Sense Amplifiers as columns, with a whole row of cells discharging into their corresponding Sense Amplifiers on each read cycle, the Sense Amplifiers then being used to recharge that row of cells. The column signals select which Sense Amplifier is connected to the output. So you don't need to read every row and column of a chip, just some column on every row. The Sense Amplifier is a circuit that takes the very tiny charge from the cell transistor and brings it up to a stable signal voltage for the output.
So why use DRAM at all if it has this need to be constantly refreshed? Because the Static RAM circuit requires 4-6 transistors per cell, while DRAM only requires 1. You get close to 4-6 times as much storage from the same number of transistors.