IIRC, an H-1B can't apply to be a citizen, you have to be a permanent resident to do that, which you can only do from an immigrant visa. The H-1B is a "dual purpose" visa, which is a non-immigrant visa that doesn't require you to leave the country before applying for an immigrant visa, but you still have to qualify for one of the immigrant visa categories and make it through any source-country-specific backlog for that category. (And the vast majority of tech-industry H-1B's are from India, which is also near the top for waiting list length in many of the immigrant categories -- including all but one of the Employment-based categories.)
The most common pathway for those who complete their studies in the US and want to remain in the country to work is to obtain a work visa (H-1, L-1, TN, etc) under employer sponsorship. And then, some of these visas permit immigrant intent i.e. your employer can sponsor your green card even though you're technically on a temporary worker visa.
I'd love to get permanent residency and possibly citizenship. The framework in place right now is tedious and frankly, outright hostile to those of us doing everything right to remain in this country. Thankfully, I'm not from one of the countries with huge visa backlogs - I can only imagine their pain.
I've been in the US for almost 10 years now since undergrad and have put down roots (friends, acquaintances, credit history, etc). It is very unfair for us to be put into the same bucket as body shop labor from India. I personally know several people who were forced to leave the US because they didn't get chosen in the H-1B lottery.
There needs to be a new visa that caters specifically to those in our situation. USCIS needs to let the consultancy companies and body shops compete among themselves for H-1B and stop screwing law-abiding international students who have devoted 4-6 (or more) years of their lives to living in the US, who suddenly might lose everything they've worked for because of the H-1B lottery.