Maybe I am missing something.............
There was another person bidding on the home - if their offer was for all cash, then they had an advantage over your offer. Apparently your offer exceeded theirs, so the sellers went with your offer. Isn't that what you wanted?
Did someone force you to make your offer?
Sounds to me like you're having buyer's remorse.
You are second guessing yourself, and trying to get back partt of that "extra" money you offered.
Well..............That's not really how it works.
You made an offer - your offer was accepted.
Now you had a home inspection. The inspection is for things you CANNOT see and Items that are of a structural nature.
The condition of the carpet and flooring didn't change - it is what it is, and you clearly saw it prior to making your offer. It is assumed that your offer factored that into the number.
As far as the appliances go...was there a seller's disclosure?
Did they state the age of the appliances?
Are they in working order?
if they are, I really don't think it is fair to ask the sellers to compensate you for that.
You're not buying a new home.
Bottom line is............You can always ask.........the sellers can say no.
Why not just be happy you are buying a home you worked so hard to get?
Tough luck if you don't like the way they look.
You could ask for money to replace carpeting/flooring. Is it that huge of an issue for you? Will your offer look worse compared to other offers on the house with this contingency?
I'm not sure "fair" is the right word. If you want these things, ask for them! You just might be surprised at what the seller says.