As I'm sure you're aware, there is a strong correspondence between procedures and records. Closures can be implemented as records holding state variables and code, and records can be implemented as special procedures. It would make sense to me that the rules for procedures and records would be the same. So it would be convenient if the result of
(eq? (lambda (x) x) (lambda (x) x))
were the same as
(define-record-type my-record make-my-record my-record?)
(eq? (make-my-record) (make-my-record))
It makes the most sense to me if both of these expressions return #f.
A similar question would arise if an implementation provided immutable records - can immutable records with the same fields be "eq?"?. Perhaps if there were a notion of an "immutable procedure", the answer could be that mutable records and procedures have identity, and immutable ones do not.