I know the minimum layer height will effect how detailed of an item you can print and the amount of time it takes to print something, but is it necessary to have an extremely low minimum layer height if you plan to print only larger objects?
I believe the Slic3r Manual summarizes this quite nicely:
A thicker layer height will provide more flow, and consequently more heat, making the extrusion adhere to the bed more. It also gives the benefit of giving more tolerance for the levelness of the bed. It is recommended to raise the first layer height to match the diameter of the nozzle, e.g. a first layer height of 0.35mm for a 0.35mm nozzle.
In other words, larger layer heights for the first layer typically gives better adhesion, and makes inaccurate bed leveling (and auto leveling) still work.
As with any manufacturing process, you'll need to learn to "use the right tool for the job". It depends on the requirements of the part. To answer your question, I would suggest using a larger layer height for the sheer fact of reducing print time on larger objects.
However, it depends on the part and how small the details are on the part. If your part has sharp edges that are required for the proper functionality of the part, then you'll want to use a smaller layer height. Or if your part fits into another part, you'll probably want to use a smaller layer height.
Another variable might be whether or not post-processing is necessary. Is this part going to be purposefully printed larger/rougher with the idea to use a Dremel later to smooth everything out? If yes, then use a larger layer height.
In short: no.
Smaller layers will make your prints look nicer. That said, in my experience, most printers can handle roughly the same layer heights, no matter what the manufacturer says it can do. With a little tinkering, you can get any printer to do what you tell it to do.
That said, for larger prints, you really won't want to lower the layer height too much. Typically, the quality difference you see in a print that's, say, .2 mm layer height (typical) vs .1mm layer height (typically high quality) is not that much different.
Note that lowering your layer height increases the number of layers in your object, so it'll take longer to print and have more opportunities to fail along the way. For anything of significant size (150 mm + or so) it's really not worth the extra risk, I'd say.