In your own home, this would be merely annoying.
In an installation where the thermostats are hard to get to, this would be very annoying. (I once had to change batteries on some that were 30 feet in the air!)
In a transmitter site, this is EPIC FAIL!!!
I was alerted to this problem by hearing the cooling fans in a large shared equipment room (the same one that awful Sprint equipment is in!) spooling up for takeoff.
There are two HVAC units in there, both had the same digital thermostats with the same dead batteries. Room temperature was at 98 and quickly rising.
Always insist on line powered thermostats for installations like this!!!