A16 system had a problem with spamming 1 action over and over to get better at something (like crafting 9999999 stone axes). This should be not possible. There should be restrictions and punishment for spamming 1 thing.
Also if you want to level Strength with my system you can chop trees, mine, fight zombies with melee weapons, break doors, break safes. That's a great variety of actions. You're not forced to spam 1 thing. If you want to spam 1 thing, go ahead. Ruin the game for yourself. Nobody is stopping you.
For the Agility just travel a lot. Explore. Going in a circle won't level your agility. It can be made to be leveled based on the distance you've traveled for the last minute (or any amount of time (idk what would be the best from balance point)). If you stay at your base the whole day, well you won't have Agility. The people that explore will.
Perception will be split in 2 trees. One will be leveled by shooting guns (Eny gun!!!)
Fortitute also requires variety of different actions.
Intellect is the hardest tree but it's not impossible.