This can pose a big problem for people who have made their homes in the U.S. for decades, diligently working, paying taxes, buying houses, and raising their children. It's perverse there is any visa that lets someone stay in the country for decades without offering them a path to permanent residency and citizenship.
H1-Bs do have a path to permanent residence and so citizenship. The problem is that the various rules around being on an H1-B make it super easy to exploit workers - which has a side effect of reducing permanent resident and citizen wages.
Compare with other countries, where the eligibility for residency is automatic for all foreign workers for have worked in that country for a given amount of time.