Various versions of such things have been suggested or debated plenty of times before. There’s definitely an issue with the current “read some books and become a world class engineer” meta, but fixing it is somewhat complicated to do in a reasonable way.
For example, why is experience necessary for something you have a blueprint for? You just need to put things together in the right way, and theoretically, the books that got you to that skill level should have taught you the necessary skills for putting it together. Making a flashlight and taking it apart again 50 times doesn’t really support being able to put together a unified power system, so there’s certainly some merits to your proposed solution.
That said, there are a few minor issues, like the current bonuses you get from skills (would lockpicking use mechanics experience, or knowledge? A combination of both?), and how a person gets knowledge for skills that are basically only experience at the high end, like marksmanship or bashing weapons.
On top of that, you risk making things over complex, especially for explaining such systems to new players.
Most importantly, to me, is how do you eliminate the grind part? Sitting there and crafting 50 flashlights to get better at electronics isn’t very fun gamewise and isn’t over realistic either. Some sort of training system would need to be implemented, and that might work quite well with your system.