Why are regular passes limited to 3 days when Army holiday weekends are often 4?

I would point out that in cases such as you mention, the correct thing to do would be to grant chargeable leave, perhaps in conjunction with a pass.
I for one don't want to take days off away from Soldiers or have stupid accountability formations with ranks full of drunks. Luckily, there is a mechanism for this in AR 600-8-10.

I do not the regs,but when i was a NCOIC i would give three day passes based on normal everyday soldiering about once or twice in 2 -3 month period and if excelled and exceed standards i would give you 4 days pass ,passes were also denied based on performance and other infraction,kept the soldiers happy.No passes in conjunction with leave was a reg and passes with a holiday were considered.

I bet they used to do 4 day passes, but some idiot took that to mean take 4 days off and come back on the 5th and arrived at around 1400 haha.