It is not the airline but the airport that is responsible for bagage handlers.
That is not always the case.In a lot of the major airlines like Delta,American,United,etc,that have a mini hub or several flights a day,generally have their own in house baggage handlers, that are part of the airline itself.Some of the smaller airlines,Korean Air out of kennedy airport for example, or an airline that only has 1 or 2 flights a day or in some cases 1 or 2 a week, generally rely on what is called a handling company.They are generally the low bidders and kind of independent contractors,that do everything an airline would do (pushback, ground services etc.) you can draw your inferences from that as to service and reliability.When I worked the Ramp at Kennedy Airport yeares ago,Virgin Atlantic was always fighting with their handling comp over lost/damaged or stolen items.(they only had 2 flights in and out a day)If you want to know if you think your gear is going to be safe in the belly of the plane,the easy way is to look at the name of the equipment and the names on the back of the people loading your plane.If it is the name of the airline or another major airline,than you are probably ok.If it is fly by night- be wary.