That was the first thing I thought of, too: Piers Anthony's notorious 40-book (yeah, just checked, it's still going) Xanth Trilogy.Wasn't this how...what was the series...one of the early fantasy series...the world was called "Xanth," was it? Haven't thought of those books in years and years.
Everyone in the world had magic. But everyone could only do 1 thing. Some useful, some not so much.
And one of them should probably be a healing spell...I feel like people are way overthinking this.
What am hearing is:
1) allow martial classes only.
2) all players get an effect similar to magic initiate. They have one spell they can cast. The dm can make it more or less frequent. You could even make the abilities at will...but you will need to be very careful with what spells you allow.