To be efficient at dehumidifying without excessive sensible cooling the system needs to be able to run the air handler at a low speed. If you're then burning natural gas or something to restore temp to large volumes of cool air it's a power-and-fuel hog. You're essentially pumping the heat-of-vaporization of the extracted humidity, but also that of the reheat coil out of the house via the AC condenser. The better the sensible-cooling efficiency of the AC system is, the more of a fuel & electricity hog it'll be running it as a dehumidifier.
There may be continuously variable speed air handlers that can be controlled for maximum dehumidification/minimizal sensible cooling, but I haven't looked into it. It's easier to pull off if both the compressor and air-handler are continuously variable over a wide range, where the air handler is running a miniscule volume of very dry (but also very cold) air. Mini-splits with "dehumidify" modes run the blower at the minimum speed, and modulate the compressor speed to keep the coil as cold as possible without frost-up. While this lowers the temp of the room somewhat if the duty cycle is high, the air in the exit stream is quite dry (dew points below 40F.) In normal air conditioning operation the exit air of the same system is in the 50s or higher, with higher dew points similar to or higher than that of your central-air system. (Very efficient for sensible-cooling.)
In modest to mid-sized homes a 65-70pint room dehumidifier with a 1.8liter/kwh rating would be enough to handle the latent load, and would be more efficient than running the AC & hydronic coil for net-zero sensible cooling, if not as efficient as a whole-house dehumidifier. Smaller versions tend to have much lower efficiency- it's worth the extra $50-100 up front, even though a 30-pinter would still be able to handle the load. If place the dehumidifier in a room with a large return-air register and cycle the air handler ~5-10 minutes per hour to redistribute & mix the air it can keep the RH & temps relatively even throughout the house.
The temperature of the output stream of a room dehumidifier should be well above the room temp, since it's extracting the heat-of-vaporization of the water it's condensing and adding it to the air stream. When it's running a high duty cycle this will raise the temp of the room somewhat.
On larger commercial systems there are many methods of restoring the temp of the dehumidified airstream with high efficiency using heat pipe technology similar to that used in evacuated tube solar thermal systems but I've never heard of residential sized systems. See: http://www.epa.gov/oaintrnt/energy/hpipe.htm and http://www.heatpipe.com/abouthpt/heatpipes.htm
Above 50%RH isn't a disaster from a health & comfort point of view, but it may aggravate those with dust-mite allergies. Above 65%RH is a hazard from a mold spore and fungal infection point of view. I try to hold the line at 60% RH at my house, and running a room air conditioner set to 60% RH in the basement (the coolest room in the house most of the time) is usually enough to keep the rest of the (warmer) house in the 50s without running the central AC at all. I have it set up to drain in to a sump rather than manually emptying the bucket. It uses between 400-500kwh/year (based on monitored performance) which is as much as a full sized refrigerator (without ice-maker), but that's largely due to a very low sensible AC load and extremely intermittent use of the central AC (fewer than 20 hours/year most years.)