Do we really need all six ability scores?

Yesterday I posted about hacking the ability scores to simply reduce the range to 0-5, and using the same, single number as your modifier.
To further simplify matters, I've been thinking about crunching the number of ability scores from six down to four. Here's my thoughts:

                                                                     They've been there since the beginning.                                                                     But I argue that the numbers down the right column are really the ones that matter.

STRENGTH: You've gotta keep strength, as it's a key indicator of how hard a character can hit in melee. It's one of the first things any kid will ask when creating a hero: "How strong am I?"
A single figure that you add to all melee attack rolls and all damage rolls is simple enough.
Lots of peolpe also confuse Strength with toughness (AKA Constitution) and for simplicity's sake I'm merging the two. You can therefore add your Strength score to your hit points each level. Constitution goes out the window.

SKILL: I'm keeping Dexterity, but I'm calling it Skill. That is a more accessible word for youngsters. It is also more accurate, because you add your Dex bonus to ranged attacks. And yet in real life, a person can be incredibly un-dextrous and still shoot a bow like a dream.
So Skill represents a person's nimbleness as well as their actual aptitude in shooting, throwing etc. You add your Skill score to ranged attack rolls as well as damage with ranged weapons.

MIND: Lots of people can't get their head around the difference between Intelligence and Wisdom. I mean, some people get it right away, but I guess they're the more intelligent players. Or is it the wise players? I'm not sure. Mind might be a better description of everything from mental aptitude to psychic toughness, magical ability and plain common sense.
This is the ability score you add your spell attack rolls if you're a Cleric or Wizard. It would also be used for perception/spot checks. It would be used in a fairly high number of saving throws against magical effects too - so it cannot be treated as a complete dump stat for non-spellcasters.

LUCK: Luck is a new one. For this I drew inspiration on both Dungeon Crawl Classics RPG and the Fighting Fantasy gamebooks of my youth. It always seemed appropraite, and somewhat edgy, when you were called upon to "Test Your Luck". It meant something arbitrary, unfair and ultimately very dangerous was about to occur. But while there would still be Luck checks and Luck saving throws, I'd also like to use Luck in a different way. The idea of luck "running out" is quite cool and has been used in both the DCC and FF systems. So perhaps each point of luck you have could represent one reroll per day. It gives players (especially my target audience, younger and new players) some get-out. But it's still a resource that needs to be managed carefully.
And when your luck runs out...

NB: I'm obviously dumping Charisma. It has its uses, but for new people starting to play RPGs, I think it offers too much of a get-out clause. Instead of relying on your character's high charisma and rolling a dice, why not act out the dialogue and get a little immersed in the action?
Of course that's not everyone's cup of tea but I think it's important to establish that this is not simply a game of trying to roll highest on a d20. And hey, if you get bogged down, you can always call for a Luck check.