The advantage with photosynthesis is that it also produces side products which are usually edible, tasty .. and perhaps useful for making furniture. Also, it is low maintenance compared to a lot of alternate options
And a lot of plants don't bind CO2 for a long time. Even trees have to be replaced by ~100 years and then if burnt or rotted they release CO2 again.
If you wait very long and you apply the right physical conditions, they might turn into oil again which was a good long term storage.