Do you trust your tenants enough that you would not get a security deposit?
In all seriousness, when you show up to your rental and there are a few fire engines pumping water on it and the Fire Marshal asks you about smoke detectors (they will ask as will your insurance company) do you want to tell them that you asked your tenants to check on them or do you want to pull out a piece of paper or print off a record of your physical inspection of every detector in the house and when you changed the battery?
Don't be the typical news report about the landlord who had smoke detectors that didn't have batteries. 85% of fire fatalities are in the home.
I don't know what it is about SDs that tenant find so difficult to handle, but about 25% of them are disabled by tenants in my rental units -- usually they start to beep and rather than replace the $1 battery, the tenant just takes the bad battery out and eventually loses the cover. A fire fatality in that case sounds like natural selection to me...