I go back to, in my opinion, the best cop chase mechanic that the series ever had, and that's MW '05. You're right, there were a lot more road blocks and spike strips in that one.
It's not that I'm oblivious to the challenges they face. With the fact that you can off-road and drive anywhere on the map, if your car is vastly superior to the stock cop cars and they have no rubber-banding, then you could simply outrun them easily = no fun. One key difference with MW05 is that MW was almost all city - there were a lot more turns, city blocks, etc. that condensed the chase. With Payback's wide open spaces, getting everything just right would definitely be more difficult. Even road blocks and spike strips would have little effect out in the desert when you can simply leave the road and continue on.
I think another problem with the current design is that even when the checkpoints are not timed, like the abandoned car chases for instance, there is still an end destination and a route plotted out for you. One of the fun things in MW05 was getting into a chase and literally having nowhere specific to go and the objective simply being to outrun the Police. In such a system, cooldown spots are a must-have feature.
After thinking about it, my suggestions for improving the current system, in no particular order are:
A) Introduce free-roam cops with the same spawn-frequency as in 2015 (which is to say fairly infrequent). Maybe they can show up during a race event once in a while, and once the race is completed, allow us to pick a speed card, collect the cash, etc. as normal, and then transition into the cop chase in progress.
B) Introduce a new class of cop SUVs specifically designed for off-road. Plop them in the desert, and make it more challenging for us even if we leave the roadway.
C) Encourage us to leave the roadway by using more Rhinos, road blocks, and spike strips on the road. NO Rhinos on off-road.
D) Bring back heat levels... this would accomplish two things: 1) Make the Crown Vic have normal performance levels instead of supercar status it currently seems to have, and 2) make things more realistic and challenging during the later parts of the game when the player is driving exotics and such.
E) Make the player garages cooldown spots. But like in MW05, you can't be in direct sight of the cops to use them, otherwise the option disappears. Since there are only four garages, getting there would be no easy task and keep chases going to satisfactory length.
F) What I would do if I were in charge of Payback, is bundle all of the above suggestions and make it one of the DLCs and call it the "Hot Pursuit" bundle or something like that. I would also include police equipment like bumper guards, roof lights and police-related decals for purchase and customization.