Travel to Himalaya but skipping Tibet?

In september/ October we are planning to visit the Himalaya. That is Nepal/ Bhutan/ Tibet. However given the Olympics/ political situation we risk not to visit Tibet as border may be closed (no visum). Hence we may not go Tibet but visit Sikkim/ Darjeeling instead or fully postpone the trip.

Did anyone visit all of the above countries and can confirm if we’d really miss a lot if we did not visit Tibet? We are looking for the local culture and nature.

We are thinking to skip Tibet as from hearsay we think it is not that authentic anymore - influenced by the Chinese, a kind of “tourist circus” - all organised etc. and that we will find more authentic culture in Sikkim/ Bhutan + see the same kind of landscapes etc in those countries.

In short: do we miss really a lot if we skipped Tibet. Do the other mentioned countries “compensate”?