How is this faulty? The degree of damage is incredibly relevant. We don't make everything that could ever cause damage illegal, because we have nothing left. Laws are a balancing act of pros and cons to society.
A car has far less visibility (they are inside a box with a few windows) will will do far more damage if they hit someone. A cyclist has dramatically better visibility (they have basically an unobstructed 180° view) and especially when going slow is very unlikely to cause significant damage (posing risk of significant harm only the the most frail and elderly).
If not requiring complete stops for cyclists leads to 1% more cyclists on the road (because their travel is easier) it almost certainly causes less harm overall due to how dangerous cars are and also their indirect health effects (both inactivity when driving and the pollution).
So no, the logic isn't faulty at all and probably one of the most important arguments.
While Amazon is awful it isn't just them. It is a systematic issue with our economic system. Our society constantly makes efforts to keep the poor poor so that they are forced to work for low pay resulting in a cycle of abuse. Basically every public company will end up in the same situation and we see that with every large company. If a large public company isn't shit the CEO will be fired by the shareholders and replaced with one who makes the company shit.
So yes, avoid Amazon, but also talk to your government representatives. The cycle will always continue until the incentives are changed. To properly exit this shit system we need to change our society and government.