Is it valid that the armor is not in the most vulnerable part of your body? What can justify it, the movement, temperature? I’ve been watching video game armor and some of them have exposed the lathe and crotch, even in other audiovisual materials like Voltron: Legendary Defender happens. Is it valid or does it only have aesthetic purposes?
No. Though, there is a caveat here. You identified a good point: You need to armor the most vulnerable places, which isn’t necessarily the same as the most vital places.
So, vital places are things like your head, your chest, your groin. Things that, if you take a 48″ piece of steel through them, you’ll die. Vulnerable places are likely to be injured.
So, armor that prioritizes protecting the outer thighs, shins, and feet, without much regard for the groin or inner leg, makes sense if your’re mounted. Your horse will protect your inner leg and groin. So, while those are vital, they’re less vulnerable. As a result, some cavalry armor does leave the groin (basically) unprotected.
An extreme example of this is boxing. A boxer will wear gloves, and sometimes a head guard, because those are the most vulnerable things that need to be protected. They don’t wear chest armor, because, while your chest is vital, it is protected from blunt strikes by your musculature and your opponent’s gloves. Your hands, however, are quite fragile, and as a result are more vulnerable (mostly from self-injury.)
This is also why you’ll sometimes see armor that prioritizes the outer arm. It’s protecting against an inward striking slash from an opponent. You’d still want to protect the chest from a direct piercing strike, as it’s both vital and vulnerable.
Another example would be additional armor on the left arm. Again, this is prioritizing additional protection where you’re vulnerable to attack from a right handed opponent.
Temperature and cost are both reasons why you might not have the best possible armor. Heavy armor will (generally) trap heat more efficiently, exhausting the user. Obviously, being really tired is preferable to being really dead, so when the option was there, soldiers still went with the best they could get. Though it is a reason, particularly in modern contexts, why a soldier might forgo armor that they felt was unnecessary. Particularly if they were serving in an auxiliary role.
Cost is a classic tension on armor. It doesn’t matter if you’re dealing with a militia, or an organized military with standardized equipment. No one has the money to outfit everyone with the best possible gear. This means that the armor someone would have access to would be limited by what they (or their armorer) could afford to equip them with. So, while a cavalry rider might benefit from full plate, they may be forced to make due with a gambeson, because the shock cavalry and heavy infantry are above them in the queue and claimed all the available plate.
So, yes, there are reasons why a character might not have the best possible armor. Characters frequently need to make do with the best they can get their hands on. That includes armor.