I wouldn't say it's a bad idea but I don't think it brings many benefits. With a separate tarp you give yourself more space underneath, lots more headroom if you want it. Having the tarp separate also means you can set it up first and take it down last, keeping everything else dry in the process, having the tarp and hammock as one would risk getting the sleeping area wet when packed away too I should think. You can also put the hammock up out of the way if you just want some chilling space for the day time.
Maybe you're looking at it as a time saving idea, but a tarp alone probably goes up faster I reckon, once that's up you can take your time with the hammock and bedding. Speaking from a kit junkie point of view, having different tarps for different seasons is also one to think about, much the same as you would choosing a tent. A big strong tarp for winter time then a lighter smaller tarp for summer trekking. You can either look at a hammock with mossie protection for summer or a basic gathered end open hammock for winter trips.
Either way you've seen the light by the sounds of it, try a hammock and see how you get on, some folk adjust instantly while others hate them with a passion.