You’re smarter than you know. Most people don’t check for “end bearing “.
Beams can fail by1) bending (extreme fiber in bending), 2) shear (horizontal and vertical), and 3) deflection. But seldom does anyone check for bearing.
Once a beam is installed, we worry about “crushing”. Crushing from 1) the applied load (usually as a point load), and 2) crushing from the reaction (at the bearing point).
Each species has a different value of fiber stress to resist this crushing...both compression perpendicular to grain and compression parallel to grain. You’re concerned about Douglas Fir (probably Larch) at the bearing points in perpendicular to grain. (Parallel to grain loading will always have a higher value than perpendicular, so we only check for perpendicular loading stress.)
So, assuming you sized the beam properly, the maximum reaction at each end for a 1) Standard and Better grade is about 2,000 lbs, 2) Select Structural grade is about 2,600 lbs., and 3) Dense Select Structural grade is about 3,000 lbs.
Douglas Fir has a compression stress value of 385 lbs. per square inch for Select Structural grade.
Therefore, the required bearing for MAXIMUM capacity for a Douglas Fir -Larch 4x12 beam spanning 16’ is: 2,600 / 385 x 3.5” (width of beam) = about 2”.
And yes, you can “back cut” the end as long as you have the required bearing, and no, the beam does not need to fit tight to the wall, as long as it has the required bearing surface.