The 6502 was intended to be run a constant clock rate and the early version were 1MHz but later 2MHz and higher. Also some of the peripheral chips became faster with time but not all of the useful ones.
With 1MHz you can put any speed of RAM or ROM in there as long as it meets the setup times for read and write for the CPU. I can put a modern 10ns static RAM in a 1MHz system typically without problem but it's not going to run faster unless the system clocking is increased.
But in the late 80s they started to use some faster chips and the 2MHz 6502B and switch clocking rate dynamically between 1MHz and 2MHz depending on the address accessed, so that slower chips could also be used. You see that in the BBC Micro computer model B. The clock changing circuitry is a bit of a *** to understand because ideally the 6502 is supposed to be outputting two non-overlapping clock waveforms 01 and 02 from the input clock and I think changing the clock rate was a bit difficult without glitches. In the BBC Micro it gets stretched by half cycles to slow down rather than just going directly from 2MHz to 1MHz. It might seem the same but you have to check the circuitry which is right in the middle: http://www.goffart.co.uk/museum/schematics/bbc_b.pdf
You can see on the schematic that it has address decoding from IC24 (LS138) through to the inverter of IC33 (LS04) and that's what triggers the clock to slow down from 2MHz to 1MHz, but it's quite complicated because the circuit with all the flip flops depends on the 01 output of the 6502 as well as the clock counter chain input.
I don't think any machine from the era can detect magically how fast the memory is and speed up or slow down, and especially using the 6502 which doesn't have a very good wait system to insert cycles anyway. It has RDY, but it's rather cumbersome.
The BBC has fairly fast dynamic RAM which is refreshed by video access. Typically the video chip is accessing every RAM row so nothing else is needed for refresh. The CPU would access the RAM transparently on every half cycle so there's no such thing as stealing access from the video system. They're accessing memory in alternation. That's what many home computers did at that time.
Also DRAMs at that time were not that critical with refresh. You can stop refreshing them for a few seconds with hardly any data corruption. That's from personal experience with 4164 and other DRAMs. The charge leaks away over a few seconds.
In the BBC schematic IC45 is selecting the row and column addresses for the RAM in a cycle so it alternates between video and CPU access: the LS139 chip's B input is connected to the 2MHz clock so the RAM address source selecting is done based on the clock state so the CPU is getting the RAM for half the time.
Back in the 80s dual-port RAMs were like 256 bytes, and really freaking expensive.