But you've got a problem: in the "walk out of the trees" scene, the walking had to start before the brain growth - and there is no advantage to bad, slow, vulnerable, bipedal walking in a grassland. All the advantages you list come after the animal is bipedal in some reasonable, efficient manner - after a good long evolutionary transition.
The initial boost has to be something other than the advantages only gained later. Humans coopted their bipedal walking for its advantages re tools, brain application, etc - but they had to be walking first. A tree ape that wants to carry something a long way over the ground will hold it in one paw and run quickly and with reasonable efficiency on the other three - or use its mouth, like most animals. It will not stagger around on its hind legs using both front paws, wasting time and energy, making itself visible and vulnerable to predators and injury, and in fact not able to carry much more.
A chimp is no more likely than a raccoon or a bear to set out on its hind legs into a savannah. Baboons came down from trees into the savannah - on four legs, as any animal would.
You are right, but some chimps do use their hands for tools, after many years of evolution, they would increase their ability to use their hands for each time more efficient tools.
When the homo-erectus started going down from the trees to the savannah, they went not far from the trees, because as you said, they were vulnerable to predators and injury.
In the savannah, they needed more and more speed to get away from the predators.
You can see the evolutionary evidence of "running for our lives" from predators in our basic emotions. When we experience fear, it is a known fact that our heart starts beating stronger in order for more blood to go to our legs, the blood concentrates in the upper part of our legs in order to run faster. That is why we unconsciously feel the need to run when we experience fear.
But this is an explosive response, it only last for small distances, that is why I say they did not go far from the trees. The trees were the shelter.
On the other hand, when we experience anger, the heart too beats stronger, but the blood goes to our arms, not our legs, so we feel the unconscious need to hit something (or someone :bugeye: ). This is the evolutionary evidence, that in order to run, our ancestors did not use the arms, but only the legs. The arms were for making tools and fighting.
Bibliography of the physical responses to our emotions:
Emotional Intelligence by Daniel Coleman