The thing about STEM is that we only need so many people in those fields. Once you have a team of scientists on something piling on more workers isn't going to make the beaker heat up any faster. Its not like once you have a mathematical proof you need a team of punch clock mathematicians to mass produce it. So like STEM degrees are great but encouraging people to choose those degrees is going to stop making sense at some point.
One thing we do need, though, is operators. That need will be around for a while, as newer technologies, even if they build AI and robotics, etc. into it, will likely need human interaction of some form.
How many people we need as operators may vary.
How broad is this "we"?
Going by
2016 numbers, 80% of US employment is in services, compared to 8% in manufacturing. AI and robotics might have some effects on services, but it sounds like you're mostly referring to manufacturing.
Full automation would be a small blip on domestic manufacturing that's already near this point, but let's say it significantly impacts overseas manufacturing. There are many ways that any given technology can impact production, such as reducing material inputs, a cheapening of the machinery itself, higher output per material input, lowering operator skill, or increasing product quality, but the most important is usually the reduction in total hours of labor required.
Here in the case of total robotic automation, it's this reduction in total hours of labor (i.e. employment) required would be the most obvious effect. Robots are still extremely expensive and undergo continuous depreciation requiring maintenance and replacement (to a greater extent than "traditional" machinery, already ludicrously expensive), but let's say the technology improves so they're not extravagantly more expensive than other machinery, or at least the depreciation costs are less than the wage reductions. This would be a highly gradual effect that in reality has already been underway for centuries, and you would expect to see the same general pattern that industrial capital is supposed to follow, where most of the owners adopt the new methods and undercut their competitors with lower prices in exchange for taking greater market share (considering how few of these competitors there are left and how much in bed they are with each other and their governments, this effect is minimized or prolonged while they just pocket the difference, but let's say competition at least eventually happens).
What we can expect then is that whatever is being manufactured is now slightly cheaper (eventually), more of it is produced, and a bunch of half-starved laborers overseas have been thrown on the streets (more news at 11) while the total profits for the owners have gone up regardless of whatever else happens (and there are probably even fewer of them around as the industry grows more concentrated).
But how does this affect Americans? We're the ones who consume most of this soon-to-be garbage, so we get to enjoy cheaper prices. But how do we pay for it? 80% of us are in services (that is, of the 60% of the population that's employed), but what does that even mean? We're certainly not "servicing" the half-starved laborers and children that actually produce most of our junk, and while we are for the most part "servicing" each other (as opposed to directly fellating the Gates and Bezos of the country), hardly any of those people produce anything themselves except "services" (if anything).
If we listen to Keynes (who I'm in two minds about) then the ultimate source of the money that we're today just shoving around and around in services is from the fund that property owners deem worthy to invest domestically along with whatever they leave on the table at the yacht dealership (plus the various means the federal government has of wringing seigniorage out of the currency markets to increase spending without inducing monetary inflation). It's not likely that they'll take those new profits and increase domestic investment out of proportion, since foreign governments willing to bribe investors and sell their populace into slavery are hardly going to be more lacking, so what does society get out of this? Some mildly cheaper goods (if the industry cartels and monopolists get around to it), while real wages after rent, interest, and taxes continue to decline, and in all likelihood we see a reduction in the total amount of table scraps that the owner class is willing to throw to their upper-middle-class creatures and trickle to the rest. And all this continues, while the poorest continue to work 60 hours a week "servicing" a miserable and unproductive society in the last industries that can't be outsourced and while the gap between "middle class" and "abject peonage" blurs further.
There are economic aspects of AI that are interesting as well, like how it may end up replacing highly educated workers and induce a great societal lapse in human intelligence (for nobody's benefit), but this rant is already running way too long.