Not if checked regularly. No different than a live trap sitting outside in the sun all day while people are at work. It all comes down to responsibility.
You don't like them, so don't use them, but don't tell me I can't or shouldn't.
A. I don't approve of using live traps in that fashion either.
B. Being in a small cage is nothing remotely like being held down in a glue trap -- stuck to a surface unable to move.
The latter is viciously cruel.
If we are going to kill animals for our benefit -- and I am not against the appropriate and legal use of snap traps or even poison -- it is our responsibility as moral beings to kill them as swiftly and painlessly as possible.