I don't see how this is any different. Other than creating 2 buckets when 1 would have been fine.
Skills
Stealth
Perception
Acrobatics
Tools
Lock picks
Healing kit
Skills
Stealth
Perception
Acrobatics
Lock picking
Healing
Except in reality what you would have is one of two things: A blank list like in 3.5
Skills
Perception
Acrobatics
Tools: ____________
_________________
__________________
__________________
Lock picking
Healing kit (not sure why this is here anyway, did you mash it with medicine?)
This is cumbersome, and takes up space that isn't needed on the character sheet. The other way would be to just list each one individually, but again, that takes up unneeded space and crowds up the skills.
Tools and skills are separated for one simple reason that I've stated before and Tormyr stated above me: tools require something, skills do not. All of the tools require you to have a specific device or object to work. You cannot pick a lock without Thieves tools. Period. Skills are something that absolutely everyone can do with varying degrees of success. Anyone can try to climb a wall or try to be sneaky, or try to remember the location of something. That's why they are bundled together and tools are not. This is why I think the proficiency system is so elegantly designed. You can simply have a section at the end where all of your proficiency's go, and each character can list which ones they have and which ones they don't. The reason they don't do that with skills as well is because of the "out of sight, out of mind" philosophy.
My basic answer is that DEX penalties should not disappear when you put on Heavy Armor.
Secondarily, from a game design standpoint armor should not limit DEX in my mind. What should limit it is encumbrance. Armor limiting is just short cut to the actual burden which is you overall encumbrance.
Well, yeah, 90% of things in D&D are just short cuts to actual things. If they went through and outlined every single nitty gritty little detail, sure, some people might like it, but the vast, vast majority would find it too cumbersome to work with. If you want, you can just say heavy armor encumbers you more and be done with it if it bothers you.
What my proposal was in the playtest was your Casting Stat in times per day. That may be ludicrous to you but it is very workable for me. You also happen to not have a cantrip blast things indefinitely (castle walls, dungeon doors etc.)
Except when they play tested, most people enjoyed having an attack cantrip that they could use all the time. It hearkens back to the 3.5 and older days, where a wizard at level 1 takes just a few rounds to run out of spells and is forced to twiddle his thumbs or take pot shots with a cross bow. Endless cantrips make the wizards still feel like wizards even in normal combat, and lets them be viable all the time. I see no problem with that at all.