No.

Are you looking for consumer grade, or prosumer grade appliances? What you think of as the "heirarchy of brands" isn't. Some brands do better at some things than others. Someone with a 2K appliance budget may think of GE Profile as a "high end" choice. Another person with a 40K appliance budget may think of them as "low end". What you think will depend on where you stand on that bell shaped curve.

Good point. I should clarify I am a consumer / amateur looking to buy all new appliances for a recent home purchase (a foreclosure). Budget is low, still looking to stay stainless steel. Under 4k.

Is it a design faux pas to have different brands? Will this hurt resale? Or is it fine because it is a bargain. As long as finishes and handles match why not?

No one gives a hoot if the brands match or not as long as they work when the house goes up for sale. Living your life for the mythical eventual buyer is for the birds. Live your life in your house for you. Mix the appliances in 3 different finishes if you can make that work in an overall cohesive design and you like that. Then just replace with "matching" $1.98 replacements off of Craigslist when you go to sell.

With a budget of 12k can I get good appliances...fridge, double oven, range, hood, dishwasher, microwave

And some people couldn’t buy their refrigerator on a 12K budget....