As an adult trying to learn to play the piano, this is all rather depressing.
There is definitely a change in the brain that happens if you are heavily exposed to playing an instrument or otherwise making music at and before 11 to 12 years of age. Adults who do not have this are handicapped like they are missing some sort of sense. The difference is like the difference between an immigrant's adopted language and that same language as spoken by their children.
The former can work really, really hard and speak quite fluently and have the grammar and most of the accent tamed as to speak very elegantly and understandably, but they almost never get rid of the last vestiges of that accent.
If you want your children to truly learn music, then hang out with and have fun with people who do music effortlessly and for the sheer fun of it. This means that you go to jam sessions at private houses. Anything that remotely smells like a performance won't work the same way. Expose them to music done purely for the fun of it.
If you want to learn music as an adult, you have to learn how to hear again. The immigrant in the first example can think he's speaking perfectly, even though native speakers clearly hear that he is not. You have to learn how to hear again. You have to become directly aware sound stimulus, unfiltered through the higher-level notions you've developed about it. Then you have to correlate that with what happens when you manipulate your instrument. Keep doing that for 3 to 5 years.
I should add that, while I was exposed to music at an early age, I didn't really take joy in it until I discovered Irish Traditional music at the age of 19. I knew back then, that it would be impossible for me to accomplish much. I just thought if I could learn just this one tune. Then I learned a second tune. Then I went through a period of time when I was feverishly listening to tapes of myself and comparing what I heard myself play to recordings of masters for 8 hours a day sometimes. Eventually, I got good enough to teach at a school for Irish Music in the US and even qualified to compete at the Fleadh Cheoil na hÉireann, which is basically the world competition.
My journey was two decades. The sooner you start, the more time you have to enjoy fluency!
I think your personal experience holds true in a lot of domains: start with something small you can wrap your head around, and then expand outward from there.
Playing like professional players is like conquering those white shiny Himalayan peaks; it may not be impossible with huge efforts, but it's more likely that you run out of time. In that sense, probably it's "too late". I started playing the piano when I was 11, but never pursued it professionally, and now at 39 I have so many pieces I want to play but know that I will never be able to finish before I die.
So, yes, if you are looking at the shiny peaks, you have to lower your expectation.
The secret is that the hidden peaks beyond the first ones are almost as rich as the shiny peaks. And you know what, most of your audiences won't be able to tell the difference between the shiny ones and those middle peaks. You can play at parties, or even participate in local concerts of hobby players. You'll be able to enjoy playing those pieces and the experience will be as satisfying.
Have you gone back to the piano as you learn guitar? It's arguably the ideal instrument for theory...
One of the hidden pleasures I've discovered about learning new things is that it instils a much finer appreciation of the thing that you are learning. For me that alone is usually more than worth the effort of learning.
Also I've learned not to push too hard and to focus on the journey rather than the goal, but that's also something I've also had to work extremely hard at.
But I take your point, and I am enjoying myself regardless. :)