Criterion Games re-imagined and rebooted Most Wanted was the last new EA published car game I have played to date (that fits the criteria of this theme). The sparse choices for customization and upgrades was one of the turn offs, another was just how the cars handled. Although I first experienced this interpretation of their physics in re-imagined and rebooted Hot Pursuit, the vehicles were a little more manageable there than here.
Free roam police encounters were possible, just run into a paroling unit and let the fun begin, or continue with the story mode and the law would inject themselves into the action there.
This was one of the titles purchased shortly after the family got the then new Nintendo Wii U, which doesn't save gameplays. However, my son still had this on his PC and advanced all the way to the end.
One big surprise was the lack of a Lamborghini Murciélago. I could have chosen an Aventador or a Gallardo, but that could have spoiled the continuity I was hoping to establish through the other games I was playing in series. Luckily, they were wise enough to include the legendary Countach....