How does 10mm/yr of plate subduction provide enough material to create eruptions?
Yes, the situation is much more complex than you make out - the generation of melt is typically caused by partial melting of the mantle wedge located beneath the volcanic arc. This process is mainly affected by the trench geometry (flat or steeply dipping slab), the local geotherm, and volatile content (water, gases etc.) of the slab or subducted material.
You're neglecting the total volume of the plate being subducted, as there is an along-trench length of the plate, as well as the thickness of the slab. 

When it comes to amount of melt generated, the localisation and upwelling of melt from the mantle wedge isn't fully understood - so it is hard to determine how many volcanic centres will be fed from the material.