If the convergent boundary is only consuming 10mm of oceanic crust per year, it "seems" like that would provide insufficient material to cause the level of eruption generally observed. I am making the assumption that it is the consumed oceanic crust that is ejected from the volcano as molten lava. It is probably more complex than that.
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.
10mm a year is a huge volume when you multiply with lithosphere thickness and length of the boundary, but you are right - it's more complex than this.
Melting is caused by the interplay of temperature, pressure and chemical composition. In the case of subduction of oceanic crust, it's the mainly the water that have been incorporated in seafloor that lowers the melting temperature and expands when reaching a the temperature and pressure of a critical depth. As it can only expand upwards, magma chambers are formed and eventually erupts as volcanos.
The largest volumes of lava are however formed by other mechanisms. The volume of material is not directly related to the impact of the eruption, again the chemical composition is the main factor (Silica content in this case).