Cap weighting is self-rebalancing: when a stock doubles, its weight rises automatically and the fund holds the correct amount without transacting. That is why cap-weighted funds have low turnover and low costs, and it is the main reason the structure won.
The criticism is concentration. A cap-weighted index becomes progressively more exposed to whatever has already risen, so a benchmark described as 500 companies can behave like a bet on the top ten.
Example: the top 10 of a 500-stock index hold 36% of the weight. A 20% fall in those ten, with the other 490 flat, takes the index down 7.2% on its own.
Related: free-float-weighting, equal-weight-index, index, index-rebalance, market-cap