I've just demonstrated that it makes sense. But, really, that's irrelevant. You're telling me that a particular arrangement of 26 symbols “makes sense”, but another “doesn't”, even though both convey the intended meaning perfectly well – as evidenced by your critique describing the intended meaning?
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Cheap means "of a low price", so a price can't be cheap, just low.
You can pay A for B, which you then pay for C. B is the price of C, and A is B's price. If A has a low value, then B is cheap, and thus a cheap price.
Pretty much all money can be bought for very slightly more money. Thus, a price can be cheap.
"Cheap X" means "an X that costs less".
"Cheap price" literally means "a price that costs less".
You can certainly say that, but it makes no sense.
I've just demonstrated that it makes sense. But, really, that's irrelevant. You're telling me that a particular arrangement of 26 symbols “makes sense”, but another “doesn't”, even though both convey the intended meaning perfectly well – as evidenced by your critique describing the intended meaning?