Oh right!
I prefer to extract the amplicon region from an alignment rather than a primer search because of one simple issue: the reality that a primer can, and often does, amplify DNA in which it was not intended to amplify. This is called specificity:
"... defined as the frequency with which a mis-priming event occurs. Primers with mediocre to poor specificity tend to produce PCR products with extra unrelated and undesirable amplicons".
That is, I often like to know exactly where my "off-target amplicons" are coming from. By retaining as much of the reference data set in my classifier, even those that may not be a great "string match" of the primer to a given reference sequence, enables me to classify more of these off-targets, i.e. less sequences being returned as "unclassified". This is my worry of using a primer match (even with adjustments to the mismatch parameters). However, that being said...
- The caveat of using alignment positions is that it assumes you have a well-curated and trustworthy alignment, in which those alignment positions are meaningful for the group(s) under investigation! That is, your gene can be globally aligned.
- Depending on the amplicon under study, e.g. Fungal ITS, using primer search to extract your region of interest is your only recourse, as some marker genes are very difficult (nay impossible!) to globally align.
In a nutshell 
, for the 16S rRNA gene data, using the curated alignment to exctract the amplicon region of interest saves me from having to run BLAST (or another tool) on most of my "unclassified" sequences, as my off-targets will be readily classified.
-Does this help?