The wording of laws is a valid technique for defining laws.
I'm afraid not. As I explained the laws do not in fact cover all possibilities, and the wording can be missing, ambiguous, or even contradictory.
You need to recognise that the referees have been over all this already. In order to do their job they need to agree on the interpretations that they will all use. Some of this gets dealt with formally: if a player catches the ball before it crosses the plane of touch, and has one foot on the touchline. everybody agrees that the ball is in touch. However initially some said the catcher had put the ball in touch, and some said the kicker (or whoever) had done so. New Zealand and Australia developed opposing interpretations so the IRB ruled that the catcher had not put the ball into touch.
There is another controversy going at the moment. If a player kicks the ball into touch just short of the opposition 22m line and it rolls on some distance, you could envisage an extension of the 22m line and argue that the ball has gone past it so the kicker has put the ball into the opponents 22. This affects whether or not the opponents can gain ground by kicking direct to touch (after a quick throw-in, probably). South African referees say he can. English referees say what matters is where the ball crossed the touchline, not where it is pickled up. This one is unresolved.
Some other standard usages are universal but not technically correct if you insist on following the wording of the law. At a ruck, the scrum half is allowed to pick the ball out (provided it is clearly one, even though the law say a player may not handle the ball ia ruck.
Some scenarios are simply not covered: the ball is kicked towards touch. A player jumps, knocks the ball back in-field and then lands in touch. How do you decide if the ball was in touch? The only law reference close to covering this simply refers to a player jumping and catching the ball - it then matters where he lands.
I could go on, but I won't. I want to make the point that trying to decide how the game should be played by looking at the laws, is not enough. Like a referee you need to not only know the laws but also how to apply them sensibly.
Referees will heartily agree with you that many (most?) laws are badly written, but their job is to make them work.
On the NZ try, the player could just push the ball forward, but instead he changes his grip to hold the ends of the ball. For me he is attempting to lift it to reach for the line. It is not clear if it does clear the ground, but I would give him the benefit of the doubt.