The presence of algae and an overnight chlorine loss of 2.0 ppm are two reasons to SLAM the pool, and you only need one.
Leaving it as-is and 'risking' it will mean that you're maintaining and managing a nascent algae bloom. In other words, allowing the free-floating algae to reproduce, but killing off enough of it that the population doesn't increase to the point of being overly visible. Managing a pool with free-floating algae will require more chlorine per day than is needed after the algae is killed.
TFPC uses algae as the "canary in the coalmine" for swimmer safety. If that is given up, extra vigilance on the bare minimum FC level is needed.