I don't think "Food crops cannot sustain the current human population" is the most accurate. I think adding on an "indefinitely" or something similar would be more accurate. The problem is that there's plenty more land and resources that could go to crops, but it's more of a problem of how sustainable it is long term.

Topsoil erosion could outpace soil conservation especially with synthetic fertilizer, but if people aren't getting food now or in our lifetime then it's not caused by an inability to grow enough crops. It's caused by companies being driven by the profit motive. It's more profitable to let food go to waste than get it to people who can't afford it.

Currently the technology is there to make more than enough crops for everyone, but how sustainable that is in the long term is not something that has been a priority. If more effort is put into making factory farming actually sustainable, which is the way things are starting to go although pretty gradually, then the only thing stopping people from getting food is the incentive to destroy/ let it rot rather than take any potential loss from not artificially inflating prices

I disagree with that. In Western countries typically half to two thirds of agricultural land are used for meat and dairy production. We have plenty of food available to sustain the current or even growing populations without depending on mineral fertilizers. Farming techniques have significantly evolved over the past two hundred years and the crop yield of an intelligently managed field without mineral fertilizers is not signficantly lower than what is achieved by conventional farming. With the added difference that conventional farming is actively destroying the soil and killing the insects that are vital to maintaining agriculture.

Modern industrial farming is not sustainable for the next hundred years, no, but there are a lot of levers to work to transform it into something that will reliably feed future generations.

One lever is amount and kind of meat in the average diet. It takes something like seven pounds of grain to make one pound of beef. Modern chicken breeds are amazingly efficient at converting feed grain to chicken meat, but even they are something like two pounds in to one pound out. Reducing the percent of meat in our diets would make our food go significantly further.