I wouldn't call it insignificant, perhaps for current fights, since nothing is exactly 'challenging'. But take for example a fight where it was healing intensive and in between a Cure to a Sacrifice your healer has the added downtime of an AA swing 'animation'. Trying to think of a decent XI example of a high intensity healing fight with not just tank damage but AoE damage to your melee's. But been a while and drawing a blank ; ; sorry

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PW was more melees needing to not be stupid so I wouldnt say it was that healing intensive. Jorm would be a decent example when it first came out but meh not what I'm trying to get across.
I guess somthing such as the healer basically had to keep spamming cure > sac > cure > sac just to keep melee/tank up.
Now add AA ontop of it.
Cure > AA > Sac > AA > Cure. It could potentially kill people due to that GCD building up.
This is ofc with the assumption SE actually brings in such challenging content(healing intensive/DPS race/Tank Swapping etc). If everything stays simple as it currently is then you're correct that AA wouldn't bring much harm.