I recall the case of Jessica Ridgeway where they (I believe) went door to door requesting male DNA. The killer actually gave his, and that wasn't how he was found as it turned out.
My point being that yes this is done, no you don't have to give it and yes it does make you look suspicious. If an investigator cares enough, they will follow the person who did not give DNA and get it with something discarded by the individual (once you throw or give something away, it no longer is yours). Even if it ended up they could not use the collected sample for arrest, if it matched the crime scene they'd know they had their person and would find another reason to arrest and get DNA again.
If more people said no, it wouldn't look weird to say no. But people get verbally bullied sometimes and sometimes people think they need to clear themselves and sometimes people think that their being cleared narrows the suspect pool. JMO.