Yes, removing the matches does reduce the value of a book of matches.

However, aside from not being able to legally mail them in some countries, it is entirely possible that the matches can ignite due to friction in some undesirable places.

Like the cargo area of a commercial aircraft.

Also, over time, the matchtips will begin to disintegrate and will bleed into the actual matchbook, which will decrease the value.

Additionally, storage and display is problematic for full matchbooks, whereas the covers can be stored flat and inserted into holders in binders.

Just too many reasons not to keep the matches.

Except for features, of course.