Coins are still worth picking up because they add to your score.
This article over at Mathematical Mischief shows how scores are calculated during a run. The formula is sort of large, but one of the components of a score is coins, which are each worth five points multiplied by your multiplier bonus.
Assuming that the calculation on points is correct (which I haven't taken the time to double check, not realistically ever will), picking up coins could be worth a lot of points over the course of a run. So while they may no longer be useful outside of each run, they can help you to keep pushing your scores higher.