Jim, there is no "truly accurate" colors. Rough estimates put ~10% of human population living with some sort of color blindness. Even for those with the very average vision, colors are always relative due to bazillion factors that affect our perceptions - not only the environments but also a person's physical condition matter.
Our eyes possess an incredible adaptability and are capable of recognizing colors in context. That is why we can recognize the same objects (colors) in daylight and in darkness alike, despite the objects reflecting different lights in some absolute scale.
I do share some of your skepticism against sRGB purists, not least because whatever controlled environment they measure the accuracy is not likely duplicated in real life. (e.g. the moment they leave the lab the same color becomes a different one) And I especially detest the argument that "designers intents" are only thing that matters when it comes to colors: Whatever the intents of a designer or an artist, once their work leaves their hands it's open to interpretation of observers. An artist cannot control what an audience think of her/his work. Moreover, as you have said, sRGB is not something represents the real world. It is an artificial standard that industry decided on in the past and won over competing standards.
Which brings us to the point - sRGB is not something "natural" or "true," it is borne out of necessity. The necessity is none other than communication. You may not like its limited nature, but nevertheless a standard is necessary so that when you talk about a color on a screen the person listening to you can identify it on a different screen. We can analogize this to musical scales as well. Modern pianos have 88 keys, comprising 7 octaves and a few more notes. Each octave have 7 white keys and 5 black keys. (Tellingly, it's called "Chromatic scale") Do they represent all the sounds or even notes that humans can perceive? Of course not. Had that been the case we would not have needed any other musical instrument than pianos.
Your preference of deeper, more saturated red (which might as well be more representative the red on a flag, for example) is subjective thing. There is no wrong or right about it. I would go even further and say Ef' the designers' intentions - you are the judge of your perception and sensation when it comes to colors. However, as we have discussed, if you were to communicate with others using colors, we need a means, a language/grammar, or a standard. And sRGB is currently the best that we've got for that purpose on mobile devices.
Will the standard change in the future so that deeper colors that please your eyes will be someday called "accurate"? No doubt. It is a matter of when, not whether. But until then, having a standard is better than not having one at all. It's not only practical but also egalitarian.