The story quests are called that for a reason, if you want a break from story, do other quests or other objectives. Story quests will indeed mostly be story, tackle them at a pace you want to do them at, just keep in mind if you do all the story quests, the game will be over at that point.

Think of it more like a GTA game. If you just keep running from story quest to story quest, you finish the game and only experience like 5% of what was there. At any point, go to any other random place than the story quests and see what else there is to do.

You can for sure spend hours shooting bad guys at any point in the game.

As for when delamain wrecks one of your cars, you are expected to have a handful to choose from at that point. But I could see if you did nothing other than story quests the whole time, it being possible to not have any other car by then. Delamain wrecked my car about 100 hours into the game for me. I had 8 owned cars by then. But I had also killed thousands of enemies by then.