They do because their promise is to match the index, not produce better returns.

Moreover, S&P500 is cap-weighted so even besides membership changes it is rebalanced (the weights of different stocks in the portfolio change) on a regular basis. That also leads to rather predictable trades by the indexers.

This sounds like a sufficiently obvious failure mode that I'd be extremely surprised to learn that modern index funds operate this way, unless there's some worse downside that they would encounter if their stock allocation procedure was changed to not have that discontinuity.

Being an index fund is fundamentally about changing your portfolio when the index changes. There no real way around it if you want to be an index fund.