I am wondering why we don't have a bond exchanges in US? Why people are happy to accept the trading with broker-dealers, instead of an exchange?

The sarcastic answer would be that the dealers prefer it this way. A more serious answer is probably that there are so many bond issues outstanding and so little liquidity in so many of them that exchange trading wouldn't work.Probably many institutions do not like the transparency of an exchange and prefer the privacy of the brokers (equity trading is moving off exchange too). Hopefully a senior member could add more.

what a stupid question

why is it a stupid question? Municipal bonds traded on NYSE till the 1920s and corporate bonds till the 40's (some still do but it's very small). I don't think there is a good reason why trading largely switched to dealer markets. I remember reading an article where they argued that it was the rise of institutional traders which reduced the benefits of the exchange. But it's probably a historical accident. I think this is also true not only of market structure but for markets themselves. It's not clear for instance why markets exists for some products in the first place but not for others.

On-the-run bonds are exchange traded on BrokerTec and eSpeed