You mention lots of what ifs, but the reality is this, in the most capitalist countries it almost never happenes that there is not bread.
Even if these large companies control much, if they had problems the huge demand would mean lots of other people would have a huge insentive to get into the market. There are lots of other companies who have the fundamental tools to get into that market (logistics, financial, connections to sellers) and so on.
Cenral planning is not a straw man, it has been one of the most powerful ideas in the 20 Century that had a huge amount of peole behind it, from top ecnomist to top politicans not to mention a huge intelligentsia. Yes the modern left does not buy these ideas holesale but the principle problem is the same, their criticism derives from the same underlaying assumtions.
> Crucially, it does not mention that during times of war, when resources are scarce, that all that the video celebrates gets abandoned and something that looks suspiciously like central planning gets adopted.
Its only partly correct that during war everything is central planned, the most effective war time economy were served by a efficent market in the background.
However you are somewhat correct, the problem is just that they are different problems. In a free society usually the goal is that everybody can live their lives according to their own wishes. Markets are great for that. In a free society that goes into a total war all people demand survival above all and focusing on that demand can constrain consumtion and focus almsot everything on one goal.
So yes, if your only goal in society is to produce bread, then having a war style economy to focus everything on that one goal, markets will lose. However if you want to be a free society where people determen their own goals, markets are what you need and want.