Many great circle routes would benefit from flying over several regions of Tibet. But…
- Mean average elevation above sea level: 16,000′ – if an emergency landing were required, assuming it was even possible, the oxygen level is negligible at most ground level regions. The maximum altitude for the average human being to breathenormally is less than 12,000′. (It isn’t necessarily fatal.)
- Radar services are almost non-existent over the region.
- There aren’t as many direct great circle routes that actually can take advantage of it. Some Russian and Chinese airlines do use the route, but the number of flights is very low.
Go visit a library that has a 3D globe and take a string and look at how many major destinations that would fly ‘direct’ between each other and analyze all routes possible. You will be shocked how few there are. Heathrow only has 4 routes that fly over Tibet.
There are plenty of tools online to help you analyze why there are so few. One big reason is the polar routes from North America to Asia do not fly direct to India. It’s simply beyond the range of most aircraft. (edit: Commentator states a polar route still operates. Only two models can do it, the B-777–200LR and Airbus A-340).
Europe to Southeast Asia routes are often routed via Dubai because its cheaper, not necessarily faster or shorter.