The largest easily available 5V flash part that can be hand soldered I found is 39sf040, which is 512kB * 8bit. Larger chips are only available in 3.3V. The PGM operates at 5V.
Going from a 3.3V output to a 5V input is not a problem, as that is still over the threshold that reads as 1 on the 5V logic, the other way around you're driving an input designed for 3.3V with 5V. That may work for quite some time, but that operates the chip out of spec, so can fail at any time. (You can insert buffer chips between 5V and 3V chips, which is what many original PGM cartridges do, but the lydz boards or many conversions don't.)
While designing my boards someone suggested to use 27c322, which are obsolete but still easily available, and can be hand-soldered and easily programmed.
If someone wanted to they could design around newer (and larger) flash chips and add buffer logic, but a lot of modern flash chips are only available in TSSOP packages that are not really accessible for the average enthusiast. They are not easy to program, either, requiring expensive adapters and programmers, so you'd have to ship the chips pre-programmed, which many people in the west want to avoid for obvious reasons.
Or you'd need to include programming logic on the boards, which would drive up costs and would be going into "multi" territory.
