Zero feet. But the real issue is not altitude; it’s descent rate. The minimum is zero feet only when not descending, e.g. sitting on the ramp or during takeoff roll. If descending straight down at Mach 1 it might be more like 3,000 feet = 3 seconds before impact.
The effort to create the so-called “zero-zero” (altitude & airspeed) seat was a huge boon for crew safety when it came out in the late 1960s. This was a time where a huge number of pilots were killed in takeoff and landing accidents and low altitude engine failures and such. Making a seat with enough ballistic oomph to keep the pilot aloft long enough for the chute to blossom without also killing / maiming him (always him in those days) was quite an achievement.
We still don’t have a good solution to high dynamic flight aimed at terrain.
You need to design a system to hold the capsule firmly in the aircraft, yet release it instantly and with total reliability when needed. And every wire, cable, hose, and duct that enters the cockpit needs to have a quick disconnect that seals reliably yet uncouples easily. Every one of those disconnects is a failure point.
The whole system is driven by pyrotechnics. Which all have limited service lives and need periodic replacement since there’s no effective way to fault-test them in place. In a capsule design all this stuff is buried in the innards of the aircraft. Fighters innards are about like the human body; there is zero empty space under the skin. Every cubic centimeter is full of something. With an ejection seat the whole thing is craned out of the aircraft as a unit to replace the pyros in the seat base. Not so easy with a capsule design.
How do you propose to have the pilot, who needs to face forwards to see what he’s doing, somehow be turned around behind the seat before the canopy opens and the wind comes in?
Further, the real issue is flail injuries. In that kind of wind your arms & legs look like one of those team pennants you see flying from cars’ windows on the freeway. Whether you’re facing into that wind or not is almost immaterial.
The B-58 style capsule is the sensible end result system. The problem is it’s slower to activate by a second to more, and greatly restricts the pilot’s upward & rearward visibility even when fully opened. Not so bad for a B-58. But a fatal flaw for an F-whatever.
The medium & longer term future is to have the pilot sitting in a trailer in Nevada where his/her biggest bodily risk is spilling coffee in their crotch. I suspect the ultimate tech ejection seat has already been deployed to production.