As long as money is no object, this will work o.k. But it is expensive. Very. Dog food is formulated to contain at least 29 nutrients (government mandate, your dog is protected from diabetes, not your kid, unless the kid eats dogfood...) and fiber and will break down... Then there is the question of small animals that will eat dog food digging and tearing things up... Possums. Cats. Foxes. Dogs (ya think). Other ways more complete and cheaper...
Far better find the high MIX of mineral source... bone meal is one, green sand, etc. and work that in and cover it with a cover crop noted for lots of roots to take up, digest, hold, and release with breakdown the nutrients.
If you can get manure from free range chickens. Bugs from the bug zapper. Fish waste. Ocean fish waste is better. Sea weed. Grape/vineyard waste. Obviously this was the process known, pre WW II and modern "fertilizers" as compost/composting. In the better run operation things were added to the "manure pile." Then, after digestion, the "manure" was spread.
The problem with modern ag is that the farmer is paid for volume, NOT quality. Yes, the plants do "o.k." with 3 nutrients, N, P, K... the rest... ignored. The "eaters" need more than the 3, don't get it and modern medicine does "well" for itself... as in "big profits."
If you doubt, you can visit John Emord's web site. Attorney Emord has been suing the feds for permission to TELL THE TRUTH about nutrition and health. First Amendment issue. Winning so far. Decisions posted under "legal events." The one on omega 3 oils and heart health was there last I looked...(and the names of the litigants who paid for the suing...) The "doctors" have us under their "heel" and are "grinding" to their profit, big profit...