Is there any equivalent to this Persian proverb? "A bad or faulty item should inevitably be kept by its owner"

Thanks, but no thanks.

This expression can be used in situations other than the ones you describe; nonetheless, it can convey that same meaning in just four words.

Note how TFD lists this idiom, and provides a meaning that is similar to your hair dryer scenario:

Thanks, but no thanks.

Inf. Thank you, but I am not interested. (A way of turning down something that is not very desirable.) Alice: How would you like to buy my old car? Jane: Thanks, but no thanks.

There's no proverb, but there's a common saying: "This thing is more trouble than it is worth." That is the closest US English idiom in terms of meaning and intention to what you asked, but there's no implication that the creator should own/use the item. We tend to be direct about our dissatisfaction with a service or product, to the point where many cultures would consider it confrontational.

Additionally, in US English, a faulty product is idiomatically referred to as "a lemon". We tend to reserve usage of that saying to mechanical objects that don't work properly, like a car or an appliance. You wouldn't, for example, refer to a person, house or cake as "a lemon", if it were bad in some way.

"You sold me a lemon. I want a refund. This thing is more trouble than it's worth."

If sarcasm and proverb usage is what you want, you can twist the classic "one man's trash is another man's treasure," by saying something like "sometimes, one man's trash is also another man's trash."

The expression:

You couldn't give it away

Can be used to describe an item that is effectively useless, such that even attempts to give it away for free are refused.

Example:

"A Park Worth Millions, and He Can't Give It Away"

(Due to high operating costs).

I don't think there is an equivalent for that exact saying, but the the object itself might be called a white elephant: something that requires a lot of care and money and that gives little profit or enjoyment. A white elephant is also said to be "more trouble than it is worth."

So your room-mate's repsonse, might be:

No, thank you. That hair dryer is too much of a white elephant for me.