Only the V7/IV has an accidental that's not a leading tone. In C major, C7 is the V7/IV and C7 has a Bb which is not the leading tone of F (that's E.) Also there are only 4 secondary dominants left, the V/V, the V/ii, the V/vi and the V/iii. They all have the leading tone of the target show up as an accidental. i.e. in C major the V/V is D7 (F# leading tone to G the V)

I agree! There's only a few keys to learn. But it was done to introduce the circle of fifths.