The one thing that stands out to me the most is that programmatic "neurons" are basically passive units that weigh inputs and decide to fire or not. The whole net is exposed to the input, the firing decisions are worked through the net, and then whatever output is triggered. In biological neural nets, most neurons are always firing at some rate and the inputs from pre-synaptic neurons affect that rate, so in a sense the passed information is coded as a change in rate rather than as an all-or-nothing decision to fire or not fire as is the case with (most) programmatic neurons. Implementing something like this in code would be more complicated, but it could produce something much more like a living organism which is always doing something rather than passively waiting for an input to produce some output.
And TBF there probably are a lot of people doing this kind of thing, but if so they don't get much press.