You might get taken on under those terms, but chances are it won’t be at one of the better payers.
You could tell the agency if you want to go down that route, and it might work for a while until either you ■■■■ them off enough by refusing to cover other shifts or until the shortage is addressed.
By assured, this shortage isn’t permanent, but by all means make the most of it whilst working the hours you want to whilst the goings good.