Breathing works, just as basic spirituality. But, further you get into cultish stuff and "spiritual" experiences because you're basically restricting oxygen.
I practice Zen and, after certain point you don't even watch your breathing. You just become aware of it. So, you restrict nothing.
Unfortunately meditation and spirituality is a very sharp and two edged sword. You need to find the correct people alongside the correct path.
In our way, there's no Spiritual Experience (TM). You just become aware of the issues in your life and with yourself, then you try to solve them. We say that "something is useless if it doesn't improve your real life in a perceivable way".
Advanced Zen practitioners most definitely do report what many would call spiritual experiences. The difference is they let those experiences go instead of chasing them or attaching much significance to them.
See for example the later chapters of "The Mind Illuminated", or the excellent "Science of Enlightenment" audio talk by Shinzen Young.
Your explanation is actually what I've intended to say. We don't cling to them. They're not important as-is and not to be chased.
I've also got my fair share (of experiences) but, I don't remember any of them except one or two odd ones. I remember them because they've proved to be some pivotal moments which my life became better afterwards.
In Zen they even warn of it.