Is it good to buy health insurance for time period between the date of entry into US and the date on which university insurance coverage starts?
Travel insurance is generally pretty cheap, especially if you exclude high risk activities like skiing and parasailing. My UK bank provides travel insurance for free and some credit cards provide travel insurance for free if you book your flights with them. If you were taking a three week vacation to the US, you should be able get insured for well under $100.

The issue is that you are not taking a vacation. You are entering the US on a F-1 student visa and possibly do not have a return ticket. While many travel insurance providers will happily sell you insurance and tell you you are covered, they will also direct you to pages and pages of terms and conditions. The key to insurance is making sure you meet all the terms and conditions, otherwise they will not pay out when you need them.

Assuming you can find reasonably priced insurance, the question becomes do you need it. Travel insurance generally only reimburses you for expenses and does not pay the bill up front. This means the benefits are often limited by how much you can afford to pay up front. There also things you can do to reduce the need to see a doctor (e.g., getting a round of general antibiotics from your doctor before you leave). Overall the answer is highly personal and depends on how you would pay a huge medical bill.