Probably it does but wearing a collar is like announcing to the world that you’re an omega which would attract more scumbags
"Hey bro, check out this new collar I bought! I heard on the news recently that omegas were being marked then abandoned, so I decided to get one for the first time. Do you like it?" "..You're an omega?"
But like the fact that he is a omega is no secret. Even the friends talking were like yeah "you an the other only omega from the department", the same at his workplace the restaurant, they talk normally about him being an omega like stating a fact. So I took like is a thing people know like common knowledge to a certain point.
Why do collars don't exist in this webtoon world? I don't know if they actually do and it's my memory failing me so I don't remember.... that would totally make these omegas have an extra protection option if they are attacked. (〜￣△￣)〜