If the Halachah is, one should not use a Kli Shemelachto if one has an alternative. Therefore should one avoid remvoing and placing items in one"s oven.
Answer:
The chumra of the Shaar Hatziyon in Siman 306 Seif 3 is only when a permissible alternative is readily available. Most people using the oven for heating or storage have no easy alternative and this is therefore permitted.