Hi emma, some of the luxury cat food is so expensive, a tin of tuna is less money than an expensive can of cat meat and you get more in it! I expect that you could probably buy other cuts of meat which will be cheaper to prepare yourself as you suggested in your post.
As a long time cat owner I am afraid I have fallen victim to my cats needs/demands and feed them on Sheba or Wellbeloved varieties. After 16 years, they now have me well trained. I have tried to resist them by making a few attempts at feeding them cheaper alternatives, but they taught me a lesson by eating a couple of mouthfuls and then stalking away in disgust. They then refused to touch another mouthful and I had to throw the lot away. Help! I am thinking of setting up a support group for us poor downtrodden cat slaves, does anyone want to join me?