the secondary side can handle 1.66A on a healthy 40va transformer, a 2A fuse is fine and either will work in a dead short situation. two drawbacks I could point out with the 2A fuse is
1) if its a multi-tap transformer and the correct supply voltage isn't wired correctly which I have seen in commercial applications many techs don't check their line side and will accidentally wire a 208 system on the 240 tap you're now dropping the usable va which will increase amperage draw and could cause contactor chatter and other issues.
2) voltage sag will cause the same as mentioned in the above. grid demand and units running for extended periods of time could pull down transformer power and cause this.
I am not an HVAC guy but I believe that's mainly the reason in the field you will find a 3A fuse installed.