I don't think that's down to either Son or Kane, their job is to cut down passing lanes, it is then the job of the midfielders to attack the player(s) that the ball is being played into. Earlier in the season, we saw both PEH and, particularly, Bentancur do exactly that, resulting in goals.
For some reason that just stopped happening, probably because Bentancur was injured. I also think that those happened when we played a midfield 3, but I could be wrong on that.
A high press would suit Kane, I think. He'll be making the same type of movement to cut down passing lanes, as he would when we're attacking, essentially identifying the right space and occupying it. It's then the midfield's job to either attack the passed to player, or find the pass when attacking, often both in the same move.
High press is more about the speed and energy of your midfielders than it is about the forwards. The exception is Richarlison, but he should work great in tandem with Kane. Passing lane cut off, goalkeeper/defender pressured into a hasty pass, midfield strike. It can be high risk, as your pressing midfielders leave gaps behind, but done properly it's high reward, the two previous examples of PEH and Bents are testament to that.