Probably not much of a difference, because probably the vast majority of the passengers who do not accrue miles (but can*) would not accrue enough miles to matter before they expired.

Remember, at most airlines miles expire with zero activity in one to three years. A huge chunk of passengers who don't accrue miles are infrequent travelers who furthermore fly a different airline each time (because they choose based on price or convenient times, and may be flying to a different destination each time served most conveniently by a different airline for each such destination) and thus are not likely to repeat the same airline even every three years.