The midpoint is the cleanest single estimate of an asset's current value, because it is not contaminated by which side happened to trade last. Nearly all execution measurement uses it: slippage, effective-spread and implementation-shortfall are all quoted against a mid.
It is also the natural meeting point for two counterparties who each want a better price than the quote offers, which is why midpoint-peg orders and dark crossing exist.
Example: 19.98 bid, 20.02 offered gives a midpoint of 20.00. A buyer who crosses at the mid pays 20.00 instead of 20.02, saving 2 cents, and the seller receives 20.00 instead of 19.98, gaining 2 cents. On 50,000 shares each side keeps $1,000 that would otherwise have been spread.
Related: midpoint-peg, bid-ask-spread, effective-spread, price-improvement