I also work designing processor intensive software, so I'm aware of the limitations of computers. And I've done weeding on farms - distinguishing Italian ryegrass from perennial ryegrass for example. That's why this whole robot idea excites me. Sure it won't happen straight away, but oneday I hope nobody will have to do such sub-human work.
amount of processing power; several thousand dollars worth
Oh that's all you're talking about? That's nothing compared to the cost of building the mechanical parts without mass production. A GPS receiver is effectively free. I have a feeling you're trying to make the software problem sound expensive just because it's complicated. 15 years ago automatic number plate recognition was unheard of, now it's done routinely from moving police cars. Car-park guards can type your number plate into their computer and their cameras will find where you put your car. Addresses on letters are scanned faster than you can blink. Sure these may be easier problems, but they have some tougher cost/performance/portability requirements.
In weeding I think there are 2 separate applications which you're confusing. One is to replace selective weedkillers that you spray over everything. The other is to replace manual weeding. I don't know what this is like elsewhere but when I was doing it, I was usually picking out a single unwanted variety from a field of one or two OK ones. Choosing between 2 or 3 possibilities is surely much cheaper/faster than comparing to a database of thousands.