You are absolutely correct. However, when people talk about "corporate greed", they usually are talking about large corporations with shareholders, not a food cart with three employees.
I find the second point questionable. Firstly, the two options you give are mutually exclusive; either they don't have to pay staff as much, or they will see lower turnover. Lower wages made up for by tips will not decrease turnover if the owner passes that on to themselves via lower wage.
Secondly, and this is a regional thing, but where I live (Oregon) there is no exemption from minimum wage for tipped workers. Workers who make tips must still be paid at least the base minimum wage as everyone else. This puts a hard floor on how low wages can go regardless of tips.
I'll acknowledge that there can be some benefit to owners and shareholders from tips, but I do not think that the tip gouging that has become common benefits a shareholder more than it hurts them via consumer frustration.