The Italian armsmaster Fiore dei Liberi gives us this delightful instruction in his section on fighting unarmoured with a sword held in two hands:

This play, where I strike you with a kick to the groin, is made to hurt you so much that your cover will falter. When you make this play you should do it quickly, to prevent your opponent from being able to counter it.

This instruction is from part of a much longer work which describes unarmed, armed, unarmoured, armoured, and horseback, combat. Then as now people drew a distinction between 'friendly' combat and self-defense. In the above section it is clear that this strike to the groin is made to cause so much pain that your opponent's ability to defend themselves (their 'cover') will falter, allowing you an opportunity to kill them.

Notice that this is in the unarmoured section, the armoured section doesn't have any groin strikes, because at the time this combat manual was written (circa 1409) armour would have made it, not impossible, but difficult, to kick an opponent in the groin, both for the attacker and the defender. Armour is not quite as heavy as many people percieve it to be, however maintaining your balance is vital, with so much metal, much of it strapped to the upper body, it is easier to be knocked or pushed off balance when wearing it. A writer of a later combat treatise, Pietro Monte, specifically advises someone in armour to 'maintain yourself above yourself' - interpreted as 'keep your weight centred and don't overbalance'. What I'm getting at is that it isnt impossible to kick an armoured opponent in the balls, but the chances of it working are low (their armour) and the chances of you becoming overbalanced (your armour) are just too high for it to be worth it.

The Tl;dr is yes, kick people in the balls if your life depends on it, but when you're both armoured, it probably is best to go with other options.