But doesn't the value of BTC go up as the reward halves? So "3 more halving cycles" should be counteracted by each coin being 8 times more valuable, no? I could very well be wrong, but that's what seems intuitive to me (I don't follow crypto very closely).
Every 4 years block reward halves, so in the next two halving block reward will be much less than fee reward, making it more and more irrelevant.
The 2140 is the date where it reaches 0, but it will be completely irrelevant in 12 years (3 more halving cycles).