I have three of the charger/maintainer units. The ones I have are Peak brand like the antifreeze. I know they just put their name on them.
I have one on in each machinery shed 24/7, over the winter months. They are four years old. I have a index card by the walk door of each shed. That card has a list of all the major machinery in the shed. I mark when the charger/maintainer was on each piece. I move the charger/maintainer every week to a difference piece of equipment. Like the combine, the JD 4960 tractor and other things that are used seasonally. I have never had any issue with any of them. I also have had way fewer battery problems since I started using them. They only charge 2 or 4 amps.
I do have one of the small "smart" chargers. I use it on the TMR wagon. I put it on every Saturday morning and take it off Saturday evening. That thing I do not trust as it will over charge the battery.
As far as worrying about them being a fire hazard. I bet that I can walk around your place and find many things that are more of a fire hazard. If you have them on a circuit breaker with a good grounded cord I would say you would be very safe.