You don't need AC to remove humidity. MVHR removes it and dumps it into the drains when the warm outgoing air goes through the air to air heat exchanger to warm up the incoming air.
So during the winter houses that aren't incredibly well sealed need humidification more than they need dehumidification.
During the summer it gets quite humid even when the temperature isn't all that high.
That's not something I claimed.
Most people in the US are only using AC in the summer (or warm season), to remove humidity from their home when the humidity outside is much higher than indoors.
MVHR seems to assume outside air is always cooler and fresher than inside air, and uses that for free cooling. Which is great for like 70% of the time. But what about the ~30% of time when it isn't there.
You don't have a dehumidifier. One of the biggest benefits of fabric first is the reduction in complexity.
I'm also going to guess that the MVHR is also not 100% efficient. It's either going to create heat to completely cool down the incoming air (hey, look, an AC, complete with dehumidification), or the incoming air is going to average out with the out going air, creating an increase in temperature.
Plus, all of those bags of mostly water are going to be expelling heat, too.
A decent MVHR runs at double figures in terms of watts, so like an old fashioned light bulb.