Might as well tag a pro and see what he thinks @Eldredge
In a natural reef the phytoplankton forms part of the basic foundation of the food chain. It converts sunlight into matter via photosynthesis. Small organisms then consume the phytoplankton and are then consumed by larger organisms and so on up the food chain. If it weren't for phytoplankton, our natural reefs wouldn't exist as we know them.
In a closed system like our reef tanks, it isn't realistic to obtain an equilibrium between the light, phyto, and organisms in the food chain. So, many of us dose phytoplankton to provide food to the smallest organisms and filter feeders (including some corals) in the system. These small organisms and their offspring then provide natural food to the corals and fish. They also assist as part of the clean-up crew. So, dosing phyto adds a great source of natural food and increases the bio-diversity and robustness of the system.
There are many other benefits observed by aquarists dosing live phyto in particular (as opposed to dead phyto) including higher pH, lower nutrient levels, less nuisance algae, increased growth of NPS corals and filter feeders, increased feeding response from many corals, increased numbers of pods and filter feeders, and help in defeating dinoflagellates.
Some of these organisms don't care if the phyto is dead or alive, but some do - they will only consume live phyto. So, providing live phyto rather than dead phyto provides food to all of the organisms including those that require live food.
Another advantage of live phyto is that it is very difficult to overdose. While dead phyto should be treated like any other non-living food because it will foul the water if overfed, live phyto will simply live in the system consuming some nutrients until it is consumed.
As far as dosage goes, almost any amount of live phyto dosed on a regular basis will be beneficial. I usually recommend starting with about 3ml/10 gallons, but you can do much more than this if you wish. Less would also be okay.
The benefits of dosing phyto will vary somewhat from system to system, and not every reefer will observe every benefit. I tend to think of phyto as a very basic food that makes the system more diverse, robust, and healthy.