What specific implications? And an important distinction isnt that you should ALWAYS follow the rules, but that you should be aware of why the rules exist and what happens if you don't follow them. Then it is up to your discretion whether following or breaking the rules will work better.
Your initial impulse is much better than what you are saying here. It's much better to understand the principles behind the "rules" than it is to follow a list by rote, and you were exactly right to ask about principles. So, let's derive some principles, shall we? Below is a four part realization in the key of A minor for every instance Sessions lists, followed by an explanation for those I can explain. If you just want the conclusion, the things you need to remember, see the bold bit at the bottom.
1. This is a typical deceptive resolution, so of course the Leading tone G# must go to A
2. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
3. I don't get 3 & 4. Think I'd have to see these in a larger context. The leap of a tritone in the bass in example 4 could make sense if it were part of a sequence of similar leaps(?)
5. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
6. If the G# went down to F it would be a prohibited augmented 2nd.
7. If the G were sharped, there would be motion by an augmented 2nd, a prohibited interval.
8. If the F weren't raised it would be motion by an augmented 2nd
9. If the F were natural there would be motion by an augmented 2nd. If both were natural the succession of 6 chords would be weak in the bass.
10. If the F were sharped, there would be motion by and augmented 4th in the bass, an interval usually avoided.
11. F# would be out of key - we're going to the relative major here, so F-natural makes sense (is in key).
12. See 11. If it isn't going to continue through G#, there will almost never be an F#. See examples 8 & 9 where the two accidentals are properly paired.
13. F isn't going to turn into F# in this kind of basic diatonic grammar.
So, the main principle seems to be: motions by augmented intervals are outside the voice-leading norms of common practice music. Eight of the above rules can be retired if one simply remembers: Don't write augmented intervals in diatonic progressions!
The second principle can be stated two ways: 1) don't raise the 6th without raising the 7th right after it. 2) Don't sharp the F when you're clearly hanging out in the relative major.
So, to comply with Sessions' rules you only need to remember two things:
1) Avoid motion by augmented intervals.
2) Don't raise 6 without also raising 7 (or, don't raise 6 when you're in (flirting with) the relative major.)