I leave mine on. Firstly, it's convenient for me to see when people like my mother was last on her phone (for safety reasons) as well as my boyfriend as we don't live together and it helps me gauge that he's at least okay especially if he is driving to/from work and I see he was online. It just gives me piece of mind that he is probably okay (I know whatsapp online/last seen can be off) if he was able to still send a quick text. I guess I'm just paranoid about my loved one's safety. Especially my parents as they are old and not street smart.
Secondly, I don't care if people see I was online and did not reply. The people who matter, knows I will reply WHEN and IF I can. Me and my boyfriend knows if there is a emergency, you call. Whatsapp is not for emergencies. If someone urgently needs me, they can call.