If it helps it go down better, think of a spearman beating a tank as a thousand guys with spears overrunning the tank unit while they're bivouaced for the night, standing in the chow line, and all their tanks are shut down, having maintenance performed.
A company of tanks is not sitting, engines running, locked and loaded for combat 100% of the time, sorry to say. Tanks are maintenance-hungry beasts, even under (especially under) combat conditions. I have crewed the Abrams, I know what I'm talking about.
Tracks need tightening, greasepoints need lubricating, weapons need cleaning, fluids need topping off, and on modern tanks, the most tedious, and necessary chore of all, pulling out the engine air filters (called V-packs) and cleaning them. This requires shutting the tank down, removing the rear deck armor to gain access to the engine, allowing the engine to cool so you can get in there (turbines get hot hot HOT), and pull the V-packs. A turbine engine sucks in about 1500 cubic feet of air per minute, and that collects a LOT of dust and grit. So during this necessary procedure, which should be performed once a day, even more often under dusty conditions, a tank is completely vulnerable.
So think of those longbowmen gacking off your crippled tanks as having them hit the armor unit unawares during maintenance after battle, and killing the soldiers, then sabotaging the actual tanks.
