1. Because the rates on brokered CDs are generally higher. If I walk in to my local bank and look at the rate board, they are laughable...still under 1%.
2. Because buying through your brokerage account is as easy as clicking a few buttons. If you buy directly from a bank, it's generally more involved. Do it in person, there's paperwork and it can take 30 minutes. Do it online with a bank where you don't already have an account and it takes time.
3. Because you have enormously more options as far as the maturity date, and the type of CD (callable/non-callable, step, even zero coupon).
4. With brokered CDs, you have hundreds of banks you could buy through on one screen. It's easy to spread your money across many banks with minimal effort. If you have a large account, this comes in handy so as not to breech FDIC limits at any one bank.
5. If you want to buy CDs in your IRA or other brokerage account obviously it will be easier and/or required to do it through the brokerage.
6. If you buy secondary market CDs, rates are not fixed, it's what someone is willing to sell for. On any particular day I can find CDs yielding 0.1% to 0.25% over the equivalent maturity new issue, even after commission. Additionally, there are a couple thousand CDs available through secondary market at any point in time, so there is much more choice.
7. With secondary market CDs rates are updated in real-time. When you buy from a bank, their CD rates are updated maybe weekly at best. Most times it's less frequently.