Pros and cons of not having PhD advisor's letter of recommendation after postdoc?
The only time that you shouldn't ask for a letter of recommendation from your PhD advisor is when you are not allowed to ask for one. This is not often the case, but it does arise in a few instances. The best-known one I can think of is that in Germany a Doktorvater (supervisor) is not allowed to write a letter of recommendation in support of an applicant whose PhD he supervised. 

Other than that, you should have your PhD advisor write a letter; it is expected by just about everyone that the supervisor will write a letter, and it will definitely raise questions for you if you do not submit such a letter. If there is a particularly compelling reason, then, you should have that well in hand at the time when you are writing your applications. Otherwise, you'll have a lot more explaining to do, and probably a lot of potential postdoc supervisors may not even bother giving your application a second look.