eq may expose implementation (it's even called "implementation equality"), but it's very useful.
Implementation equality lets you use an object as a key in a lookup mechanism which adds external associations with an object (which could be de facto properties of that object, or links to other objects). You cannot do that with an equality that deems similar objects to be equal.
eq does not mean "in the same box". In many implementations, it means "same bit pattern". Two unboxed integer objects (fixnums) are eq if they are the same integer (bit pattern). However the ANSI Common Lisp standard doesn't require small integers to be eq to themselves. eql is used for testing for "same number, and eq equality for everything else", which means that 95% of the time you want eql if you think you want eq. The 5% you're sure you're only comparing symbols, or else objects such as structures or CLOS objects for their identity.
Implementation equality lets you use an object as a key in a lookup mechanism which adds external associations with an object (which could be de facto properties of that object, or links to other objects). You cannot do that with an equality that deems similar objects to be equal.
eq does not mean "in the same box". In many implementations, it means "same bit pattern". Two unboxed integer objects (fixnums) are eq if they are the same integer (bit pattern). However the ANSI Common Lisp standard doesn't require small integers to be eq to themselves. eql is used for testing for "same number, and eq equality for everything else", which means that 95% of the time you want eql if you think you want eq. The 5% you're sure you're only comparing symbols, or else objects such as structures or CLOS objects for their identity.