(This started as a comment, and evolved into a lengthy explanation. TLDR; AI is not what the OP thinks it is, and the question shows strange misconceptions about what ANNs are, how they work and what they can do.)
What is Artificial Intelligence?
Artificial Intelligence is a sub-discipline of computer science; by and large, artificial intelligence plays within computer science the role that philosophy plays within science: that is to say, if we know how to approach a class of problems, then that class of problems gets its own sub-discipline (such as numerical calculus, linear programming, or sorting and searching) and if we don't know then the class of problems is shunted to the wastebasket sub-discipline of "artificial intelligence".
As time passes and we discover ways to approach various classes of problems they move out of artificial intelligence to acquire sub-disciplines of their own; for example, thirty or so years ago chess-playing and grammar checking were considered to belong to artificial intelligence; but now there are efficient ways of doing both, so they are no longer considered to belong there. We see this happening before our eyes with image classification and face recognition; ten years ago both those classes of problems would have been considered to belong to artificial intelligence by any worker in computer science, but today we are very close to having excellent efficient methods to classify images and to discriminate between human faces so that today most practitioners would consider them to be distinct sub-disciplines. As Wikipedia says (quoting Douglas Hofstadter, the author of the famous Gödel, Escher, Bach), "AI is whatever hasn't been done yet".
I have no idea why the OP believes that "we don't really even understand how neural networks work". This is patently false. We know perfectly well how artificial neural networks (ANNs) work; that's why we can use them successfully. It may be the case that the OP is referring to the inability of a neural network to provide explanations for its results; this is indeed a big drawback, and it's inherent in how they work; and we definitely know what they can do and what they cannot.
ANNs are good for classifying stuff, where the "stuff" can be anything that can be represented in a computer. They can be trained to discriminate between pictures of sheep and pictures of goats, or between phonemes, or between grammatically correct and incorrect sentences. That is essentially all they can do, and you need a new set of parameters for each and every application. The big drawback is that the result comes "as is", with no explanation, unless one is ready to accept a large set of numbers (representing the weight coefficients assigned to the myriad inputs by each node) as an explanation; and when they fail and misclassify the stuff, they fail spectacularly: Ars Technica had a delightful article on how self-driving cars (which use ANNs to recognize traffic signs) can be confused by stickers pasted on stop signs (quoting a serious study by Ivan Evtimov, Kevin Eykholt et al.).
The OP says that "neural networks can be programmed to do only one thing at a time", which is trivially true. But the OP forgets that an ANN is a mathematical structure implemented in dedicated hardware as a large matrix of weight coefficients; you can have as many active (loaded) ANNs as you want working in parallel, and you can have many more stored on disk ready to be loaded unto the hardware. This is not a serious limitation.