I am too young to have been there for the digital vs analog debate, but I understand that things being digital was not always obvious. The reason digital won is because, very crudely, to double the precision of a digital circuit you just give it wider registers (scale horizontally), while to double the precision of an analog circuit you have to more than double the precision of every component of the system (scale vertically). Digital was/is cheaper. But, as my electronics professor put it, "every circuit is analog at some level".
The big problem is not precision in the abstract, the big problem is that analog is just about impossible to replicate reliably en masse. You could build 1000 digital circuits and they'd all come out and operate exactly identical or not at all. Your analog circuits are going to come out in a bell curve roughly between un-usable and perfect with component variation and parts count as ingredients. You can mitigate this to some extent by very careful design and pre-assembly component selection but not all the way.
The way to deal with that in the analog world is an expensive process called 'trimming' where you use adjustable components to get you where you want to be. But trimming makes the circuitry sensitive to being bounced around and makes it more sensitive to temperature changes if you use the cheap version and the expensive version (digital circuitry masquerading as trimmable analog components) puts the horse behind the cart if you wanted analog then you're no longer getting it (but some kind of quantized version of analog).
For some circuits this is all more important than for others.
Finally, digital reduces the component count and so increases reliability and decreases cost. Software is hard to make and expensive but once you have it the marginal cost of reproduction is next to zero.
Digital, once the bugs are worked out has none of these issues and so lends itself much more to economic mass production.
I'd go even further and say that you can increase the complexity of digital systems exponentially, and create functionality that just can't even be imagined in the analog realm.
But another feature, not inherent to all digital circuits but certainly prevalent, is the ability to reprogram them. For me to change an analog circuit might take hours with a soldering iron. You can load a whole new "circuit" into a digital system at the push of a button. This in turn changes how products are designed. Analog functionality is used sparingly where needed, and gotten working early in a project. The digital system is left with some flexibility, e.g., allowing changes to made later in the project without drastic hardware revision. The mantra of the analog team, at the 11th hour of the project, is: "Can we fix this in the firmware?"
