I teach college classes on automation and robotics. Allow me to take a page out of my book for the broad implications of automation and where/how it SHOULD be implemented and why it's done that way.
Put simply; the question isn't whether automation is cheaper, because it's not a digital scenario. There's costs associated with all types of production, so the actual question is "at what point does the automation BECOME cheaper than the alternative" which is generally manual labor.
There's also different types of automation, and each one carries its own advantages and disadvantages. Robots are considered "Flexible Automation" because the robot is multi-functional and re-programmable by definition. Robots are a common go-between when trying to save money through automation, while now being nailed down to ONE SPECIFIC TASK. Robots can adapt to a certain level of change, but not as easily compared to doing it by hand.
The alternative is a dedicated production process that cannot be [easily] altered in the future. If you built a machine that picks up your object then moves it to a destination, but can ONLY do that, without any sort of programming...that's not a robot. It's considered Hard Automation due to the lack of flexibility. (remember I said multi-functional and re-programmable). It's easier to work with a robot compared to Hard Automation, but the throughput is higher with dedicated hard auto.
Loading and unloading a piece of production equipment is extremely easy for flexible automation like robots, but it only makes sense under certain situations. If you're making the same part every day, day after day, or a family of very similar parts all sharing similar hardware...it would be extremely easy to automate the process using a robot. And it would pay for itself after an extremely quick period of time if you were in production with your keyboard or whatever other item you want to discuss. HOWEVER, if you're continuously making different items, or the variety of workpiece is sufficiently non-uniform, paying a person to load/unload would likely be cheaper.
The "next level" is called Hard Automation and is comprised of mass production equipment that is purpose-built to accomplish one single task without adjustment. Think fast moving and highly repetitive (cutting operations, die equipment, presses, bottline lines, industrial ovens, some types of boxing equipment, etc). The workpiece has to be uniform, so it's often fed by manual labor or flexible automation whereas the repetitive hard-automated process itself is cheap and fast.
Once upon a time I made this graph which depicts the cost-per-unit of products manufactured by all three types of production:
The chart is generalized, but shows trends in cost-effectiveness as the volume of components increases. A set of example volume markers have been labeled V0, V1, V2.
1. Initially (volume v0), manual labor is much cheaper than any type of automation.
2. Once the volume of V1 is reached, flexible automation becomes cost-effective, and its cost-per-part continues to decrease.
3. Once the “mass production” volume of V2 is reached, hard automation becomes cost-effective and the cost-per-unit approaches zero.
The perfect example is production of a small item like a bolt or screw. Great video for a bottle cap.
Imagine if they were all CNC machined one by one. It could be done that way, in fact you could even have a person load and unload the machine, or have a robot do it. Or you could have a piece of hard automation load the machines, but it would be limited to ONLY one specific size material (as shown in the video). The more generalized the equipment, the slower and more costly it would be per unit. Instead the hard automation is able to produce many finished units per second.
Bottomline - there's no way to argue "can it be automated?" because the answer is always yes. 20 years ago, creating an automated process was a long drawn-out activity that involved custom-made machines and extremely expensive hardware. These days it has become cookie-cutter for a huge portion of the industry, because the industry wants everything to be plug-and-play. We're pretty much there for many types of tasks like sorting, simple assembly, and machine tending. The barrier for entry on automation is lowering all the time. Some of today's kid toys are inadvertently teaching them how to do the same things.
To directly tie things back in with your specific task (PCB tending): it depends on how much is being spent to have you do the job versus how much it would cost to install a piece of automation to do it for you. How many units are being made and how quickly do they need to be produced. Is there any chance of changes in the future, if so then those would need to be accommodated. Then it gets into the age-old debate on "new versus used" when it comes to equipment. There is no one true answer of yes or no, instead you have some math to fill in to determine where the tipping point lies.