There are a number of benefits to using supplemental air handlers with your hydronic system.
Air handlers allow geothermal heat pump hydronic systems to provide cooling and dehumidification for your home. The chilled water is circulated through a heat exchanger in the air handler, and a blower circulates the cooled air through air ducting in your home.
Why use air handlers rather than the in-floor or underfloor piping already present? Because cooling cannot be done effectively with hydronic piping. Without air handlers, very little dehumidification is possible, and any condensation that does collect on the pipes is a hazardous nuisance that is hard to dispose of. Also, since heat rises, either the pipe needs to be on the ceiling, or the air needs to be stirred with fans. Using air handlers to distribute cooling, instead of the hydronic floor piping, neatly solves these problems.
Some homes have a very large amount of heat loss, and the hydronic heating piping cannot transfer enough heat when the outside temperature is below a certain point. Air handlers can be used to supply additional heat from the water-to-water geothermal heat pump (or from electric duct heaters, an existing oil or gas furnace, a wood burning stove, etc.) when this happens. It can also be used to help the heating system recover more quickly from setback temperatures.
Coupling air handlers to your system will allow your home to be heated with a much lower water output temperature. This allows the water-to-water geothermal heat pump to run more efficiently, saving more money on your heating and cooling bills.
Finally, air handlers allow air filtration and purification, which hydronic systems otherwise lack.