Yes, quote could be eliminated entirely and you could just quasi-quote everything, but it could introduce subtle bugs. For example, any list literal containing the symbol 'unquote could potentially get expanded by mistake.
(= x "foo")
`((unquote x))
=> ("foo")
Common Lisp improves the situation slightly by using the internal symbol SYSTEM::UNQUOTE to represent a comma, but that's still not perfect.
