The textbook I'm using explains the it is "impractical" to have a normal distribution for all values of $\sigma$ and $\mu$, hence the standard normal distribution table.
To me, this simply doesn't ring true. We could have a phone app, to generate a distribution for $\sigma$ and $\mu$, then highlight the desired area.
But, is the standard normal distribution important beyond being a time-saving calculation tool? There are so many important concepts in statistics and so little time that it feels like a wasted opportunity to teach outdated calculation methods.
HOWEVER: Until there is a revision in the way that we teach elementary statistics, my students must learn these methods. The standard normal distribution is ubiquitous in math and science education. Students may need to learn about it to understand how other people may talk about statistics.
What should be the future of paper tables?