Sphaero
Struggling to explain his genius to the hoi polloi
Not being in the CL in the season concerned was due to circumstances beyond the club's control (i.e. Chelsea fluking it), but the point is that Spurs have finished in the top 4 twice in recent years, which gives the lie to your claim that Kane Spurs can never experience CL football with us.
Yes, Spurs have shown the ability to occasionally qualify for the CL, so it is certainly not impossible, but just not that likely.
If Kane manages to keep his form on his current level and maybe even builds on it, he will become a player who will at least look for a club which offers regular CL football. Players of that calibre might stick with their clubs for a season without it if they see it as an abnormality, but if the outlook is less promising they will be gone sooner or later.
If Kane develops as hoped, the only hope of Tottenham for keeping him is to become a stable part of the league´s top 4 and probably even do at least decently in the CL. Otherwise I don´t see him sticking around longer than 2017 or 2018.