As a ceramicist it'd be difficult to 3d print with because the kinds of temperatures you can reach even with heavily fluxed silica is still extremely high. I fire bisque at cone 04 which is approximately 1060C / 1940F and that's considered low fire, only extremely heavily fluxed glazes (usually pure frit or equivalent) melt at that level.

Putting 3d printing concepts on the table, though, you could definitely see something like a sintered bed printer using a laser to print it, but then you wouldn't get anything close to the standard FDM style print.

I also assume directional solidification is really important for basalt, like for glass fibers and others. That's hard to achieve for bulk objects but easy for fibers.