It's all part of the greater problem with the towing operation: what's the hurry?
Getting the waste barge out of the planetary orbit might require great haste, there being no time to separate the saucer. Plus, it would look really bad that these shielded Starfleeters evacuate their civilians when the unshielded folks down on the planet are suffering.
But after the barge is out of the immediate vicinity of the planet, Riker could just as well return next month or next year to finish the towing. Nothing obvious is to be won by plunging it into the star anyway, except for the star acting as a honking big quarantine marker: if it radiates under tow, it will continue to radiate inside the sun as well. So, any location suitably marked and suitably distant from the planet would be equally good, and any location outside the immediate low orbit should be good enough for the next few centuries already. Riker might be under obligation to finish the dangerous job of towing the disintegration-prone barge, but he isn't under obligation to finish the job in the 24th century.