Don't really know enough about neuropsych to be qualified to comment, but even so, here I go
As for computerized testing...I've heard that concern voiced here before. Maybe there are super-complex tests out there I'm not aware of, but for the most part, I don't feel like administering a test is a doctoral level skill. Maybe something semi-structured like the SCID is. Certainly the clinical interview should be done by someone with extensive training. However, you could probably train a high schooler to administer any fully structured test as long as they were sufficiently motivated. It takes time, it takes training. Right now, these are generally what computers are doing.
Interpretation is a whole different ballgame. Computers suck at it. Check out a PAI printout. Will this change sometime in our lifetime? Maybe, but I don't see it happening anytime soon. AI is just not there yet. So far, computers aren't even at the state where they can displace bachelor's level psychometricians. That will have to happen DECADES before they could even stand a chance at displacing doctoral level neuropsychs.
As for the general state of the field I will add this. I think anyone who wants to be remotely respected as a psychologist in the upcoming decades is going to need to be strong on biology, neuroscience, etc. The time when psychology was closer to philosophy than to the sciences is over. We have ignored biology for a long time, I think we still tend to ignore it far more than we should, and its getting embarassing. I don't think going into neuropsych automatically allows one to escape this problem, but I do think neuropsychs are better off than average when it comes to understanding the biology-psychology relationship. I know I'm not alone in thinking that relationship is going to be the key over the next several decades.