The biggest reason I hear is it costs too much to buy fruit and vegetables. Living in the UK it can be expensive to buy some fruit but we also have an amazing array of seasonal produce that very reasonable.
We have found that by eating a mainly homemade vegan diet excluding all meat and most dairy from our diet we can eat a rich array of fruits and vegetables. When compared to buying processed food such as cheese, fruit is similar in price.
Our total shopping bill has been at most the same as before but most months has been less than when we brought milk, cheese, eggs etc.
Another reason I hear is people don't have the time or energy to cook healthy meals. I agree some cook books have long convoluted recipes that take a long time and lots of ingredients but there are loads of simple recipes available that don't take as long and are designed with cost in mind.
You can also do simple things like making food in batches so you have it ready to heat up when you wouldn't have time to cook a full meal. Sometimes we make salads that we can have with different meals throughout the week.
Sometimes the best meals we have are the simple ones!
The real cost I think we should be thinking about is the cost of our health, how much do we value our health compared to our shopping bill?
I would prefer to spend money now on good organic whole food that keeps me well rather than paying with my health later, even if it means cutting back on other things.