Being consistent is sometimes enough, but not always. If you're doing a quilt consisting entirely of 9-patch blocks, for instance, you will be fine with any size seam allowance. However once you start mixing in angles or blocks that have different numbers of seams, you need to patches that measure correctly in order to have the whole thing come together accurately. Quilt patterns are designed with a 1/4" seam in mind, but the theory underlying this is that you're living in a 2-dimensional world. However, fabric and thread are not 2-dimensional; they have some thickness. When you take two patches that are 2" square and sew them together with a seam that is exactly 1/4" you hope to wind up with a rectangle that is exactly 2" x 3.5" (losing 1/4" of each 2" square in the seam). However you are going to wind up instead with a rectangle that is 2" x something less than 3.5". How much less will depend on the thickness of your fabric and thread, because these things cause some of the fabric to be "lost" in the seam. This is why the "scant" 1/4" is important, and how scant depends on the thickness of your fabric and thread and how well you can press the seam flat (which again depends on the fabric and thread).
Even if there were no need for a "scant" 1/4", being consistent is not enough when you are dealing with more complicated blocks. Suppose you decide to sew 1/2" seams instead of 1/4". If you make a 9-patch it looks fine. If you make a 4-patch it also looks fine. But now take a 9-patch and a 4-patch that were supposed to be the same finished size and try to put them together. It won't work, because there are 2 seams going down the 9-patch and only one seam going down the 2-patch! This is an exaggeration, but the theory holds even if your seams are only 1/16" too large or too small.
The lesson to take from this is that you need to measure your block as it is formed to be sure your units are measuring correctly. The seam size needs to be adjusted so that the *finished* patch is the right size.