Cheap? No. Going on dates is very expensive actually.
Gross? No. Two lonely horny people taking care of each other's bodily needs. Reproduction is still an essential part of human nature, even if babies don't happen every time we do it now.
Being used? Only if you aren't mature enough and don't know how to set boundaries, which is necessary for serious and exclusive relationships as well.
Safety - There's this thing called condom these days, prevents most kinds of STDs. That risk of still catching something still exists with any other person too unless you only go for virgins. HPV affects 50-60% of sexually active populations in most countries and is even asymptomatic mostly, go read up on it.
False cases - mostly a cause for worry for men and not women. It is a risk as much as your partner turning out to be too clingy or a stalker. There's all sorts of risk in dating/marrying generally as well.