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I cannot find any place in CLtL where it specifies what will happen if you
try to do:
 (DELETE thing list :COUNT NIL)

The discussion of keywords on p62 suggests that keywords get initialized to
NIL if not supplied.

On p254, the notation used to describe DELETE is ambiguous. Because the
syntax is described as

 DELETE @i(item) @i(sequence) &key :from-end :test ...

and not

 DELETE @i(item) @i(sequence) &key from-end test ...

it's hard to tell whether the author meant to imply that these keywords would
default to NIL if unsupplied or whether there might be initial values that
he wasn't telling us about.