I had similar experiences to these in my current game (which has been quite a challenge). But the results are due in part to my stupidity rather than the RNG. In one instance I had cut off all the enemy's resources, and they couldn't build cavlary to attack me, leaving me able to close in on their cities. I had landed a few tanks behind enemy lines to pillage resources, and lost two of them to longbowmen. Not quite spearmen, but.... Anyway, these bowmen got to be a real pain. I lost one tank to a longbowman. A turn later, I had an elite tank produce a MGL, only to have a bowman run out and slaughter the tank and destroy the MGL! And at one point I foolishly left a stack of artillery unguarded; these were used to attack a city and like a bonehead I moved the mech. inf. guarding it into the city. A longbowman ran out from a neighboring city, and destroyed a stack of 15 artillery!
I had bombers by this point... in each of these instances, I diverted them from bombing the enemy cities to pound each longbowman into dust.