We're a long way off from that. Things like that have been around since the 90s/early '00s, but they're more for OEMs and QC work than for repair use. Something like this, for example: huntron.com/products/probers.htm
They used to be huge, but it looks like they're almost table-top now. The idea behind them is that you use a VI (voltage vs current) curve signature (pic related) to validate boards. You connect one probe to ground and another probe moves between various points, while a computer analyzes the VI curve to give a pass/fail response.
The problems with this are two-fold:
1. A computer doesn't have judgement. If you set something to pass up to a 5% tolerance, things fail at 5.0001%. Things don't need to fail at one hundred millionths of a percent, but a computer doesn't know that. So you end up with people chasing their tails using instruments that may or may not be as accurate as the machine that made the call, may or may not have been calibrated recently, and so on.
2. These VI machines work on set parameters. By this, I mean that if a VI machine has however many voltage ranges, but a particular one isn't enough to accurately find a problem, and the next higher range may destroy whatever it is you're testing. See my other post about the board full of op-amps: At ±12V, a board was verified as good twice. At ±15V, it turned out that there were two ICs whose power pins were shorted - a difference of only three volts in each direction. Another time, I saw a guy working on a board full of 4000 series logic. Almost every IC on the board was warped - the lid was bubbled up or in a few cases blown right off. CMOS logic can run on anything from 3-15V. He powered it up with 5V and half the ICs that were visibly bad or blown still tested good!
Machines can't make judgement calls like that. And as far as desoldering and soldering, forget about it.
If you're into computers and shit, one thing that you might be able to get into is what's called a Pinpoint machine, made by Diagnosys: diagnosys.com/en/products/pinpoint-range2/pinpoint-ii-r2
It's a standard Windows-based PC, but it also includes multiple power supplies, and a series of cards that contain relays, transistor circuits, FETs, and so on. On these cards are various connectors (pic related). You can use it as a meter, as an oscilloscope, as a VI tester, or you can build your own test clips for connecting to anything from 4- to 40-pin or even larger DIPs, SOICs, QFPs, PLCCs, and so on.
You get a board in front of you, and create a layout like you would in any standard CAD program. But as you go, you identify each device with a part number (CD7400N, SN74LS04AN, etc.), and the Pinpoint has built in code that it runs when you clip on each IC and hit the button. It then does a series of tests (Power, Voltage, Shorts, Opens, and one or two others, I forget) and determines whether or not the part is good. It's primarily used for testing digital ICs, but creative programmers can use them to test analog and mixed signal devices, or even build connectors to test entire boards at once.
Still, a lot of operator judgement is needed. If a device fails, the operator has to figure out why. Is there another part in-circuit, like a diode or a capacitor, that's causing it to fail? Will slowing down the test from 4.0MHz to 3.5MHz or even 1MHz help? Should you alter the code to change your HI/LO voltage thresholds to accomodate for pull-up or pull-down resistors or an out-of-tolerance power supply? Maybe you need to use a different connector on the card, or a different card in the machine…
If fucking around on a computer and pouring through code all day to fix a typo is your thing, then being a Pinpoint operator (or programmer) might be your thing.