You realize, of course, he owns the stadium and has a suite. He can easily watch without subjecting himself to the crowd.
Billionaires don't sell multi-billion pound assets because the plebs yell at them.
Too many come from the, in my opinion, erroneous perspective that he doesn't care about results, either. Lewis may not, but Levy has labored day in and day out for 20 years at this football club. He likely (wrongly) thinks that he's the only chance Spurs have of overcoming the state of inequity in football. That the club needs him to maximize revenue, minimize expenses, stay afloat and continue to catch up with the pack financially.
He's not a good chairman, but I don't think for a second he's a disinterested one. He attends more matches than anyone in his position at a club of our level.
It's also unlikely that any oil state is interested in Spurs. The MO for oil state football purchases has been to buy cheap/distressed clubs. That's City, Newcastle, and Chelsea. Everton if they continue to teeter and come undone will be more attractive. Our PSR doesn't matter - the FA has shown themselves to be weak kneed in enforcing those rules against clubs with political pull, which is what the oil states have. 1 call round to some MPs and No. 10, and the FA suddenly finds other more pressing matters. The only clubs that will ever be punished by PSR will be the lower table unconnected clubs trying to spend their way up (like Villa).
Spurs would likely cost £4B before Levy would consider it. It'd take another £1-2B on players to elevate them to the level desired. £5-6B to get there.
You can buy Everton for £500M, with a nice new stadium, plow £2B into players and leapfrog Spurs with half the investment. We're simply not as attractive as some think.
Levy isn't going anywhere. When Spurs do sell, it will be him and an investment bank buying out Lewis. He'll die in the chairman's seat.