Did the budget balloon and delays rack up? Yup, and if you read about why you will see that it was basically unavoidable. A private business would have canceled it at the first roadblock (depriving us of an INCREDIBLE scientific tool).
And for the actual launch and deployment, the cost of the instrument meant that a very high success rate was very very important. Go ahead and look up the success rate of space X launches and tell me you would put a multi billion dollar tool on their rocket. You need someone who can spend more money, even a lot more money, and guarantee success.