Well it is mostly not worth the money. One of the biggest benefits of wide bandgap materials is the higher breakdown voltage. But that should not be an issue for logic circuits -- one should not ever reach the breakdown voltage.
Another benefit of wide band gap devices is the low on resistance. This would also benefit logic circuits, but the benefit would be much smaller because logic circuits move much less current than power circuits. Switching speed would be a definite benefit for logic, but is it worth the cost.
The biggest driver of profitability for logic circuits nowadays is large wafer sizes and small feature sizes. Wide band gap semiconductors are nowhere near silicon in this regard. In silicon carbide the newest thing is 200 mm wafers, available only in a few fabs, while silicon has been on 300 wafers for many years. As far as feature size, Silicon Carbide is absolutely giant compared to silicon.
It would take hundreds of billions of dollar to make silicon carbide features as small as silicon, and nobody wants to pay it because currently silicon carbide is much more useful in power applications where you want large features.
The issues for gallium nitride are similar, except that gallium nitride may narrow the cost gap with silicon because it is currently made by merely depositing gallium nitride on silicon wafers, so a lot of the production technology is similar to silicon. But then again when one starts pushing the edge of the leading nodes of silicon, I am sure there a lot of differences between gallium nitride and silicon will appear, so using gallium nitride will not be that simple.
So you may see gallium nitride appear on some mixed signal chips or some logic chips that are far in the lagging edge (e.g., MCUs?). But currently there is so much demand for this stuff (both SIC and GAN) for power that using it for logic is way on the backburner for everybody.