Maybe we are not using the same Shapr3d version? I noticed when I reproduced your video, mine is 3.33.0. The idea to scale the solid is a great one to test it, but my findings are different…
With a triangle base of 5000mm and a 4 decimal Extrude draft angle (19,4712) I get a side with a 4μm error, see photo:
I tried to reach the limits of the software (which I found out is a 1km square) but since I couldn’t extrude more than 500mt, I resolved with a Tetrahedron of 500mt base. This, with a Extrude draft angle of 7 decimals (19,4712206) gives an error of 1μm, see photo:
Since we have still three decimals to go and we are at the boundaries of the software workspace (you see the earth is flat beyond 
) that appears to me to be truly enough to work with peace of mind… 
I fully agree that using (and rounding) infinite numbers adds errors not present in a pure geometric solution, but seems to me that within Shapr workspace (but THIS version, yours seems to give much worse results) they are beyond perception.
Very interesting conversation, started with a weird draft angle (for me) and progressed to a 500mt Tetrahedron… 