I usually minmax since I like to play on the higher difficulty settings. But even from a RP standpoint, it doesn't make sense to me that my Assassin is not good at killing things. Therefore RPwise he SHOULD be good at killing things.
Same for any other role in the game. Why would a Wizard be bad at casting spells? Why would a Fighter be bad at fighting?
A couple of answers to what you wrote. First, not every assassin is Artemis Entreri (ie: an unparalleled master of martial combat.) Some are just good at sneaking into places, ambushing a target and escaping unnoticed. Assassins don't typically engage their marks in duels, they just kill them when they least expect it. What I'm getting at is that just because a character may be an excellent assassin, that doesn't necessarily mean they excel in melee combat.
To address your other queries: WWhy would a wizard be bad at casting spells or a fighter bad at fighting? Nobody says they would be. Just because you don't have 18 intelligence, doesn't make you bad wizard. The tendency of min/maxers however, as another poster said, is to have a wizard with very high intelligence with 6 wisdom. From a RP standpoint, that makes no sense but from an min/max standpoint, it makes perfect sense as they typically are only concerned with increasing their primary statistics at the expense of the others.
Assassin in 5e D&D translates to dealing a lot of damage. That's how you one shot your target since you do not have an ability that allows for an instakill like in (I believe) Pathfinder.
From the Assassin under Roguish Archetypes entry in the 5th ed. PHB:
Death StrikeStarting at 17th level, you become a master of instant death. When you attack and hit a creature that is surprised, it must make a Constitution saving throw (DC8 + you Dexterity modifier + your proficiency bonus). On a failed save, double the damage of your attack against the creature.
That ability will indeed deal a lot of damage and would probably instakill most targets but it isn't something that can be done in the midst of combat and it certainly doesn't make the assassin a great martial combatant which was my point. You're not going to want to sit there and trade blows with an equal level fighter for instance as you will likely lose that battle.
Also, a Wizard with high INT and low WIS can make sense RPwise. It is a mad genius that is highly talented but does not care for the consequences, he only wants to discover more about magic, even if it means causing harm to himself or others. This would be my take.
Meh, that's a bit of a stretch. I would submit that a wizard with 6 wisdom would probably have killed himself years ago while still in training by doing something like trying to summon a creature from the lower planes without adequate protection measures. I mean it's possible, of course, just highly unlikely. Far more likely is the wizard with 6 strength because they never took their nose out of a book throughout the entirety of their training.