It's about speed. Wolffia can double in size every day whereas the fastest growing woods can take years to double in size.
Also, while Wolffia is human and livestock edible, to make it safe for consumption would require precise control over the growth media to prevent unhealthy buildup of contaminants whereas using it as feed for self-growing building materials, clothing materials, and packaging materials is a viable alternative.
It would require little by way of energy, be a carbon-negative process practically from the start, help supplant a more dangerous industry (plastics and foams) with a safer one, and the waste products would be compostable organics.
Further, Wolffia prefers mildly acidic, highly carbonated water for optimal growth, so you could boost production by percolating carbon-heavy air into the water, and for secondary utility you could also grow fish in the vats to provide additional fertilizer for the Wolffia while also farming a secondary source of income, or failing that you could incorporate these farms into wastewater cleanup plants, allowing them to help provide clean drinking water for cities while also absorbing carbon out of the air, locking that carbon into static pieces, and then growing useful materials from them all in one fell swoop.
So, yeah, wood has its uses and is a great carbon sink, but for sheer quantity and speed Wolffia and mushrooms have it beat.
There is a problem though, and that is getting Wolffia to grow in a farm is a difficult process that we do not have mastered. It can be done but it takes time and skill to get started, and would require maintenance above and beyond traditional farm work, but if that problem were solved then it would be a good thing all around.