Toei had given the explanation why HaouKen Xross Saber doesn't use Kamen Rider Falchion's MumeiKen Kyomu even though it was used to create it. They have stated that Kyomu has a different relationship when compared to other Holy Blades.
The reason is connected with Kyomu's position on the Sefirot. That is the Da'at position. It is described as "It is a Hidden Sefira. It is a Sefira from a different dimension. The hidden meaning is enlightenment, awareness, 'God's true intention' which was hidden by God in the universal thing and which was being searched by a Wiseman based on his ordeals". Hence Kyomu is a hidden sword which makes it different from the other Holy Blades. Due to this Kyomu doesn't exist inside Xross Saber.
To be more specific, MumeiKen Kyomu sits in a position that connects with all the other positions. But its position is not supposed to exist. It is an additional position that helps unite everything as it connects with all the Holy Blades from its position.
TV-Asahi states that Xross Saber can "maintain Harmony by returning the surplus power released from it (Xross Saber) into the Void". The void that is referred to here is clearly Kyomu which is the hidden power.