I think it's safe to say he wasn't going to be taken alive. It was just a matter of how long. This guy knew from the second he gunned down a helpless stranger his life was over. Perhaps he wanted that extra push to end his own life. His life was in disarray, but nothing that couldn't be fixed. He choose a really selfish and senseless way to really drive himself to the point of no return.
He messed up big time and knew he was running out of options, even if he had the ingenuity and skills to evade police - I doubt many contacts would be willing to help him hide out. Many people may have tried to prolong the chase, but his time was clearly up.
It's sad these days how many troubled people wish to end their own lives by killing others. Like they need justification to take their own life. In turn, instead of having a basic case of suicide the person is forever vilified as a killer, effectively ruining many lives.
Ultimately this country really needs to focus on better mental health services. Not everyone has a huge, stable family that will offer all the support needed to prevent stuff like this. Part of the problem is our health care system - easier access to facilities is a must at this point.