In my second main programming job, in a physics lab starting in 1968, I had two hours twice a week (during changes in experiment) plus one weekly maintenance day to work with the computer itself. The only medium was punched paper tape, so I would load the editor tape, read in the source tape, use the no-monitor teletype to make the hundred or so changes I had handwritten (in pencil on legal pads or previous printouts), print out new source tapes (typically 5 pieces each about 50 feet long), read in the compiler tape, have the compiler read in the new source tapes and print out a binary tape, then finally read in the binary tape to see if things worked. Each cycle would be about an hour, so I was ahead of the once-a-day people, but I got very good at foreseeing the consequences of changes.
It is very useful to become capable of being precise, taking alternate paths based on logical distinctions, producing correct results by multi-step methods, and refining and extending an initial solution until it fully meets a set of needs. Programming teaches these skills directly in the context of concrete "make this happen" activities, in contrast to math classes which teach these lessons (if at all) indirectly in the context of abstract "follow the rules" activities. A lot more people will be successful at answering the question "does this program do what I want it to?" than the question "is this sequence of statements true?" Even if the goal is to produce more people skilled at abstract math, we would get more people there quicker if they gained the mental discipline that naturally arises from programming prior to dealing with most mathematical abstractions beyond numbers and simple variables.
Our emerging knowledge of genetics implies that our self-engineered descendants a few centuries from now will be very much more capable (if our lineage makes it that far). This will be especially true of the subset who leave high-gravity planetary surfaces and the dangerous neighborhoods of stars for better real estate in deep space. Their descendants, perhaps based on superconducting neurological systems (cold is a feature not a bug for quantum effects) and with the size that microgravity enables, are unlikely to have much to say to entities on our current level.