"So empirically the most significant factor is now something else."
That "something else" would be the 40%(!) of the EU budget that is spent on agricultural subsidies.
That "something else" would be the 40%(!) of the EU budget that is spent on agricultural subsidies.
Your choice of words however would mislead people into believing that 40% of European national budgets are devoted to farm subsidies and that EU subsidies exceed US subsidies by a similar proportion. This is grossly untrue.
The difference is the US consumer realizes far less benefit. e.g. corn receives far more subsidies in the US than in the EU yet somehow is still more expensive to the US consumer.
What the US does have is an aversion to enforcing anti trust laws, tariffs designed to disadvantage consumers (eg on rice), a taboo on regulations and effectively no consumer advocates in government.
That is not actually the case.
And there is plenty of "food accessible to the people". Too much of it is far more common than too little nowadays.