I’ve thought about that and actually think it could work. The impact to the system seems to be:

• Additional leak paths – If you are switching back and forth between rigid and flexible PVC, then you are making more connections and each connection brings with it the potential for a leak. This isn’t a deal breaker, of course, it just means you’ll need to be sure your connections are solid.
• Changes in elevation – In addition to going around bends, flexible PVC is good for changes in yard elevation. My yard, for example, is fairly slanted towards the street in the front and is banked in the back to improve drainage. Again, this isn’t a deal breaker, but you should look over your plan to be sure you aren’t expecting rigid PVC to make elevation changes outside of its capabilities. These changes wouldn’t be indicated by a "plan" (or top) view of the system!
• Freezing concerns – Although my plan involves the use of drains at the ends of the lines (which are still working successfully two years after installation), I’ve always taken some consolation in the fact that the flexible PVC would have a little "give" to it in the event of a freeze. I’m not sure how much leeway I have in this regard, nor how much of that you’d lose by using rigid PVC on the straight segments, but it’s worth your consideration.
  If you’ve considered the above and rigid PVC still seems to be a good idea, I say go for it. I hope you’ll return and tell me how it went!