Unfortunately, this basic problem may be used as an excuse to stop trying, in the interest of enabling other outcomes. Because there is no simple way to resolve the issue, the best-effort solution is adopted, and after a while it becomes the standard. The original defect remains lurking in the background, if somewhat forgotten if not ignored completely. The fact remains, however, that big orders have so much of an effect on the VWAP calculation that the original argument for making the calculation at all becomes less relevant for that big order.
But how does this affect the market? There are two main types of traders executing baskets: those who are trying to make money by being right in about some outcome they have predicted, and those who are facilitating -- that is, they have promised, for a management fee, to provide a match between a vehicle, such as an ETF, and some underlying basket of securities. Both must be "in it to win it," or get in and out of their carefully crafted baskets simultaneously, without failures to buy or sell portions of the basket diminishing the application of their strategy.
However, the trader who is trying to make money on the trade has a natural limit on the overall price he or she will be willing to pay for the basket, while the facilitator may not be so constrained. As long as the facilitation trade is small enough so that it doesn't much affect the larger index, there might be little difference in market effect between the two. The scenario changes rapidly when the "tail" of large capital allocations coming into the index by way of the vehicle operated by the facilitator begins to wag the "dog" of the underlying index.