With a more fluid level and skills system would at the same time mean changes to the perks system. If skills were raised by doing actions in the Fallout world when perks and traits would have to be designed around that organic growth.
Taking the example from earlier. Sneaking based perks would only be available at certain levels but what if a sneaking perk require a certain quest to be completed which in the story narrative explained why you would gain such a skill or how about needing more than one skill to be at a certain level mixed with a certain S.P.E.C.I.A.L requirement.
What if there were backgrounds and a personal character story and choices you have made affect what outcomes not only happens in the world, other character you meet but how your character evolves personally. Be evil and get a more deadly, gruesome sneak perk or play nicely and get a buff based sneak skill to help those around you. The possibilities and combinations are endless.
Finally, what if certain skills could be lost through actions, quests or random events. If you lost a limb could you still be a master at stealth? Would lock picking still be possible if you only had one arm? This leads onto the next suggestion in What 10 things should be in Fallout 4.
4. Perma-death and permanent change