Just a thought:

You can only do a petty or felony every so often so that you can "lay low while the heat wears off" correct?

Well once you fly to a new city there wouldn't be any heat on you.  Why not set it so the felony and petty timers clear once you fly?  Possibly even the attack, but don't want to push it.

It's not a tremendous change but, I believe, adds a realistic factor.  If you KO the PO in New Orleans they won't be looking for you in St. Louis.

Any thoughts/suggestions on the matter?

I like it. RP wise it fits, though a point some people might make is that it would bring more money into the game... Which is something they're against. I don't like the idea of the attack timer being reset, but the Felony and Petty are perfectly plausible.

I think you have a good idea in one respect, but flawed in another. Say you were to fly to your home city... Indeed they would be looking for you there RP wise. As far as the money is concerned, thats a very minimal amout for there to be haste in.

Being as minimal as 1 petty/1 felony for each flight availability my opinion is that it would not be a significant enough benefit to warrant the change. (My opinion)

The petty and or felony itself may not be worth the change, but ultimately you might be flying into a city to do a MUC, which would potentially benefit you a hundred thousand or more. That'd definitely be worth it, in my opinion.