Unless your terms of use specifically state that all content posted on the site becomes copyright of you, all the content remains the copyright of the object’s creator. So you “trying to protect them” is pointless, as you are trying to say their logo design is your logo design! There is no point in you paying for copyright of every post, every logo etc that appears on your site. It would be an endless and expensive job, especially if it isn’t actually your copyright! If you delete the post or article, that’s your choice, the creator still has the copyright, your website is simply additional evidence of when it was first published.
Suppose I answered a question here about what a drop-shadow on text looked like, or what a two-tone logo looked like, and created a quick logo to demonstrate this, or took an existing design I’d made for a client, and posted it on a forum, it’s still my copyright or the client’s copyright. If SitePoint then deleted my post - let’s say I lost my temper and used rude insulting language when someone said that’s a bad design - the design is still my copyright. It is up to ME to protect my designs, not you.
Now in the case of writing an article for a magazine, or online site, say for SitePoint, the magazine or website will not own the copyright unless they buy the article and also state that I am transferring my rights to them. And this is what often happens. Not always though, and I have re-written articles and had the re-write published elsewhere a second time (book reviews, software reviews, product reviews, etc). I have even seen identical articles appear in different magazines where the author didn’t bother to re-write it, but as it was their copyright, there was no need to re-write it, and clearly they had retained their rights when it was first published. But if the first magazine had bought the rights as well, they couldn’t do this, a total re-write would be required.
So if I sold an article and retained my rights, it is MY task to take the plagiarist to court, not the task of say Sitepoint. But if I sold an article AND my rights to Sitepoint, they can choose to take a plagiarist to court. And they would collect any damages, not me. And they don’t need to submit each article to a copyright office to establish the copyright is theirs, as it would be in the terms of me getting paid by them.
In the case of a company running a website or magazine, they have copyright signs to show the articles now below to the company and not, say the website editor, or the fashion editor or the managing director or someone else. so the company can sell the article etc without asking someone else’s permission.
The advice on righting your site’s terms of use is very important, but all your worries are irrelevant and unnecessary, unless you are intending to sell on the items appearing and want to take the copyright away from the creator.
Early on when I first tried freelance writing to earn money, I had my first article plagerised (but not word for word) and didn’t know I could complain and take them to court. Several years later I knew more and when two of my articles appeared under a different name, I complained immediately and got paid. It was an unethical editor who took over a magazine whose editor had moved to a new job, and he dug up a few old articles, stuck some random names on the articles, and produced a new edition of the magazine quickly. Probably pocketed the article fees too, and on my complaint paid me with his own cheque book. When he was finally sacked, the magazine paid dozens of authors money owed, without even demanding proof in my case, they took my word over the phone, said just tell us how much you want, and paid what I wanted, as they were very annoyed with the editor as well, and admitted I was not the only person complaining.