It is technically an error. Over the years I have been told by various priests and choir directors that you only sing the Irmoi at Matins. When Canons are sung at other services, they are not sung.
This is because the Irmoi are really only a model melody, used to remind the chanters how to sing that ode. (Canon composers base their hymns on existing Irmoi from the Irmologion, laying down the musical pattern from existing hymns.) In Greek (and well-translated English texts) all the verses of a canon are sung exactly the same as the Irmos, with the same syllables and word emphases.
The Irmoi are sung at Matins because we no longer chant the full text of the Biblical Odes (except during the Triodion period—weekdays during Lent). The Irmoi still reference these Biblical texts, even if the rest of the troparia do not, so it's nice to keep those Biblical references. But the full Biblical Odes were never sung at the Paraklesis, which is a simplified service, and they are directed to a specific saint as a prayer of supplication, so there is no reason to sing the Irmoi.
But you're right, in actual practice the Irmoi are often sung, at least in English-speaking countries. I think this is a misunderstanding about what the Irmoi are actually for, exacerbated by English texts that do not always have the same musical patterns as the original Greek texts.
So, the Small Paraklesis canon should begin: Most Holy Theotokos, save us! By many temptations am I distressed...
But often it begins with the Irmos, Traversing the water as on dry land...
These differences could be chalked up to "local variations". It's certainly not a big deal, but I personally prefer them to be left out.