The Gemara already suggests to only eat meat once a week (Chulin 84a). Some rabbis still advocate that (like R’ Lazer Brody). If people did that, then even if it was processed it would be unlikely to cause cancer.
The problem is today people eat tons of meat and cheese on a daily basis. Jews never ate like that historically, and it only became affordable after factory farming and subsidies made it possible in the late 20th century.
This is an area in which we shouldn’t emulate the goyim who happen to be living around us. Let us eat peas and lentils and bread and cucumbers so on, the daily staples we’ve been eating since the time of Tanakh.