One of the main reasons I started using an inflation bag is because my very first Neo-Air had issues with the reflective layer, and moisture seemed to make it more of an issue.
So I've been using an inflation bag to minimize the amount of moisture in the pad as well as not having to blow 20 STRONG puffs. (It usually only takes me about 5 squeezes of a bag full of air, the bag being a light trashcan liner (draw strings cut out) with the AirTap to hold the bag on the pad while squeezing the air in). Then like Tipi, a few breaths to top it off.
BTW: Amazon has about 10 of the Therm-a-rest Air Taps in stock. They are in the expensive side ($19 compared to only $12-15 being the original full retail price). https://www.amazon.com/gp/product/B004NBF9Z8