The spawn location after exiting the game and re-entering is sort of based on the save point locations. Some are valid for game restarts; others aren't. It will spawn you next to the most recent one that is valid.
I don't have the exact rules figured out for which are and which aren't. But take into consideration that there are several "start of the level" points. So which should it choose? And since not every level has a New-U machine, or since maybe you got to the area but didn't find the New-U, it can't spawn you at one of those every time. Or maybe you were playing at one, then someone joined, walked by a spawn point further back, then you exited before getting to the next one. But maybe that save point wasn't a valid spawn location. What if you're in another player's online game in a zone you haven't accessed yet in your own game; where should it spawn you when you go back to single-player then? It's not going to spawn you so you are stuck in a zone out-leveling you so you can't fight your way to a New-U station.
I haven't tested to figure out the exact rules for how it picks them yet. But feel free to edit this answer once we do — if we feel it's important enough. I'm not sure if I think it's a big deal; most areas don't take that long to fight/drive through unless you're under-leveled for them.
In summary, yes, it is by design that you don't always spawn at the exact last save point you walked by; but it isn't completely random either. It spawns you at the most logical point based on a spawn-point rule engine of some kind.