i m pretty sure both SMN and SCH can apply DoT without issues
i never force healer to dps
but when i heal, i found it boring just standing there
when i heal, i first observe how my team do, may be after 1st boss. i have confident about my party
i will drop DoT and some attack spell, but i would first do it without cleric stance until i m very sure
i dont play SCH much, not sure how it compare to WHM and AST
yet, i always find there are time allow me to at least drop some DoT when playing WHM and AST, unless the tank pulling all mobs from start to first boss
