No, I doubt very much precognition will ever make structured learning obsolete.
In your example, there are a couple problems - one is that your precognitive will not understand the process just because she sees herself doing it in the future (even perfectly). So, she can twist the knobs and push the buttons, but will have no way of knowing why that produces the result it did, or how to change the process when she got or wanted to get different results. One example is, watching and copying a click-by-click walk-through of, say, how to call person X (on this phone) will let the seer...call person X. On that phone. Not let them call person Y, or Z. Not send a text message to person X. Not receive a call from person X (or Y or Z). Or receive a text message from them. They can't check their voicemail, or return calls, or input contacts. They can't even repeat the same action, a call to person X, with a different brand of phone (buttons in wrong places, or different operating system, etc)
She can eventually learn all these things, by blindly memorizing the sequence of each action and slowly piecing together patterns with logic and extrapolation - which is a slow and inefficient way of learning anything, as compared to learning the reasons underlying the actions that need to be taken, and how and why the parts work together to get the result. Its a lot easier to learn to read a map than to memorize and extrapolate from looking out the window from the passenger seat - and it is too easy to not even try, and let the gps navigate for you, until even a drive you've made weekly for years is impossible without the gps telling you what to do.
The other problem is that precognition is...nonstandard. For example, how easy is it to turn on and off, how difficult is it to show exactly what the precognitive is looking for, how much information can be taken in via precognition, how easy is it to remember it...
So your precognitive would have to be a perfect precognitive, they would have to be able to specifically and reliably call forth the exact sequence of events needed to make the "whatever" work, whenever they needed it to work, they must always call up successes - or else they would perfectly reproduce future failures, they would have to learn it somehow for it to be in their future. They must be getting the information at the right rate to successfully copy it, and the right information to boot - that is, if they call up a vision of a future when they are comfortable enough to speed through the process, or when they use shortcuts that they haven't set up yet (example: pre-programmed contacts), or even use a different method (example: a future device or different app or even an update they don't have yet) they may not be able to successfully follow along and make it work with what they have in front of them.
So to make structured learning obsolete - not just not unnecessary for a specific character, but obsolete... you need perfect control over your precognition, you need everyone ever to be precognitive, and with perfect control over that precognition, and able to learn the information (perfectly) via the methods the precognition can provide (visual images if "visions", extrapolating from specific to general, using logic to work out the gaps between what's shown and what's needed)
So, yeah, I wouldn't call being able to mimic a string of actions from the future "operating" the machine, I would consider it the person getting walked through the (specific) use - even if the person walking them through it is themselves from the future.
And you have a bigger problem... seeing and mimicking a specific series of actions may be enough to, say, use a smartphone - it is nowhere near enough to make one. Not enough to design, or manufacture, or assemble one. Or program it, or design apps for it, or troubleshoot when things go wrong, or fix it when someone messed up at any previous step, or any number of other things. For those kinds of things, you need to understand what it is, how it works, and what it does. Even a vision of the (future) blueprint is useless unless you know what all the markings are, to be able to faithfully reproduce them ("Oh, you needed a value here? I thought it was a smudge!" or else "and what does that abbreviation stand for?") Or maybe person X has a correction or alternative to person Y's vision-ed blueprint, but the vision didn't show corrections, so should it be altered or not? You need to know how to read the blueprint, and which materials to use and how to get them, and how to put it into production, who to talk to, and a host of other things.
In short, you need knowledge. You need to learn things, and teach them. You need people who can work together. You need people to have ideas, develop them, do the underlying research (scientific study results via precognition? ah, NO). And really, the best way to get these things is by some kind of structured learning. Classes, groupwork, projects, innovation, methods of doing things - it might, perhaps, be different from they way education is structured now, just like memorizing is much less important in education now than it was historically because of the easy access to facts via the internet - but it will be structured somehow, because that is the easiest way to make this education standardized, to make sure all the basics are covered, and that people will have the skills they need.
Bonus question - without that there is a genuine question of who runs the world? I mean, if people are just repeating what their visions they will do, if they don't need to learn anything... who regulates that world? Who determines allocation of resources? Who decides what the visions teach them - some people are better at some tasks, or have different abilities, so who decides who goes to which jobs (and which jobs are prioritized), who regulates the industries or the markets, or checks for environmental and safety hazards, or makes long-term decisions... who fails, for heaven's sake, when they have to know they will - but what world is this of no one tries?
Are you picturing a silent world, where everyone is running on some hive-mind - or actually a pre-planned future-vision-dictated-world, but there's no practical difference, is there - everyone just knows where they need to be, what they need to do, because precognition told them so? where people just walk into jobs they never trained for (or even applied for, because the visions say who will succeed therefore who bothers to apply) and start working, repeating sequences of actions that they don't understand towards ends they don't recognize? Do people act out whole sequences of unalterable, meaningless events, or do they just skip it because everyone already knows, because everyone can just precognition the events and conversations and the results? Meetings where everyone has already precognition-ed the information, mouthing apologies when everyone already precognition-ed the explanation?
Yeah, the only way precognition replaces (structured) learning is by replacing cognition. You don't need to learn, if you don't need to think - just obey the visions. Obey. Obey