In practice, how often do U.S. pharmaceutical companies start clinical
trials before obtaining their patent from the USPTO?
I'm not an expert at this, but I think the answer is companies pretty much never start a clinical trial before applying for a patent. You need to disclose (publish) quite a lot of technical description about the drug to get a clinical trial approved and you need to file your patent applications before public disclosure of the compound. There is absolutely no reason to wait for the patent to be granted. A patent, when granted, provides protection from the grant date of the application forward for 20 years from the filing date. If the patent prosecution (period from filing to grant) is excessively long due to the USPTO delaying things than there may be a patent term adjustment to account for the extra processing time. As Trish points out there are other provisions in law to compensate for excessive regulatory (FDA) approval time.
Patents typically take something like three years from application to grant although this can vary quite a lot. Drug development is generally much longer on the order of 10 years or more to get to market. It would be advantageous to delay filing a patent application to obtain a longer effective protection, but then the company would be taking the risk of someone else patenting the compound first. Since patents now go to the first to file this is a real risk. I'm not sure what your concern is with "long patent application delay" is. Since any potential infringer would also have to do clinical trials and obtain FDA approval, there is no real potential for a lost sales.