One problem is infrastructure- how does one cut, process, and transport enough lumber to meaningfully affect homelessness or fire risk, and not build up an equivalent carbon footprint? I suppose an idea would be to construct the homes where the lumber is, but then you run into a host of other problems: building a housing development miles away in the middle of brushland exposes the people in it to increased higher fire risk, and would still require a significant investment in infrastructure (and thus carbon output) to put in place. Lets not forget that California is still undergoing record draught each year and there's still plenty of other vegetation at risk here- fire risk can only be mitigated so much by this sort of deforestation.

I was going to suggest burying the wood, but my guess is this would just increase methane emission from microbes, which is far worse than the CO2 released by burning.

I think controlled burns are still the best option at the moment.