Not "quite often" but always I think.

Sometimes we miss even more than one equation.

C

_{7}H

_{6}O

_{3} + C

_{4}H

_{6}O

_{3} C

_{9}H

_{8}O

_{4} + HC

_{2}H

_{3}O

_{2}(salicylic acid + acetic anhydride -> aspirin + acetic acid)

4 coefficients, but only two independent equations.

Because we have a homogeneous system (Since we always have a+b=c etc. and never a+b=c+2) of linear equations and such a system would always admit all zeros as a trivial equation. So a unique solution would mean all coefficients zero.

So the fact that we get a non-unique solution (before applying the smallest integers constraint) is a feature and not a bug. If you ever got a full rank matrix, be worried!

Good point

But I am not convinced - just because there exist trivial solution doesn't mean there is no other, non-trivial solution. I have no time to investigate now, but I have a feeling I have seen reactions with a full rank matrix.