A lot of Westerners have this romanticized idea of Buddhism, specifically Tibetan Buddhism, when it's had it's fair share of issues throughout history, just like any other institutional religion.
One of the many reasons I initially embraced Tibetan Buddhism was this exactly - mainly ignorance. I left the religion in severe disillusionment about a decade ago. Going to Dharamsala a few years after that and living there for a while really reinforced that for me.
A lot of starry-eyed Westerners really lose their illusions there, I think. I learned a lot from my Tibetan friends, several of whom are monks or former monks, and laypeople. Not to mention what I learned just from my own experiences. What goes on beneath the surface is... shocking, to say the least. I can't really go into a lot of details about my personal experiences, but man, they were intense. I had it drilled into me that whatever I thought was true before was pretty much wrong.
But, I still see a lot of value in the most basic teachings of Buddhism, and there's really no reason to complicate them or make them dogmatic, which is what's been done in most surviving forms of Buddhism. Like you mentioned, organized religion is also not for me, but after having experimented with a lot of different types of spirituality I know at this point which things work for me and which don't. So I do like you, just kinda pick and choose practices I like and which work for me and discard the rest. I still like to explore and experiment and learn.
It's worth noting that in Dharamsala there's effort to separate political leadership from religious leadership. Not everyone agrees, but most people of the younger generation who are culturally aware see the value in this. So I think with the government-in-exile you'll see a lot of progress toward the modern.
In Tibet though, the population density is low - people are spread far and wide, in isolated mountain villages and across plains. Many of the people are still nomadic (does that blow your mind or what). In accessible areas there are schools that the Chinese built, which often try to drive a wedge between children and their native culture, forbidding them to speak Tibetan, for example. It's possible for those children to get a relatively decent education but, it comes at a cost I guess you could say.
The people are generally quite poor and live simply. Children can get a free education, plus room and board, if they join the monastery. A lot of families send their children there simply because that's the only way to feed them and ensure they will have a good quality of life. This was the case with all of my monk friends, who joined as children because their parents just couldn't afford to raise them. Three of them gave back their vows as adults when they escaped to India. One is still a monk. This is not a decision they took lightly but in fact something they all struggled with deeply.
It's easy for us to say that people should reject their religion but we have the perspective and education to understand the situation as a whole. For many Tibetans still in Tibet, they do not have that privilege. You might be really surprised to know how isolated many Tibetans really are from the world at large. They were born and raised into their religion and fiercely believe it (same as a lot of Western-born Christians, for example - indoctrination is hard to shake). So it's not as easy as all that if you are a Tibetan person.
That's not to say I think Tibetan Buddhism is serving Tibetans well, but I do think, it will not be easy to change the situation. They are in a hard place for a lot of reasons.