I appreciate your concern, but honestly with the type of content I’m going to be posting it would be very undesirable to have to come up with titles for each and every post and it’s more than just quotes that I wouldn’t want to have titles on. That was merely only one example. I do not want titles to show up on the archive pages either if it’s a post that I’d prefer not to have a title on, or on any widgets. However, I can, and am willing to create custom url slugs for each post, for bookmarking purposes, but that doesn’t mean I actually want that displayed as the title anywhere on the site. As for the archive page, featured images will show up there to help users distinguish between pages, so I can definitely include those. I also have a plugin that will show featured images in the post manager in the backend so I can more easily manage posts without titles.
You do include a warning for the option of not displaying post titles at all that you should include a default thumbnail for posts without a thumbnail, so I don’t see why the same thing couldn’t apply? Though I believe you can set the option to turn the excerpts into links as well, so a thumbnail might not be absolutely necessary if excerpts were included with the link option selected. In any case, as far as I can currently anticipate, the posts that generally wouldn’t have titles would have images that could be used as thumbnails, and this includes the quote posts (I have to turn them into images for use on certain social media sites like Instagram/Pinterest).
If you decide that including such an option is not in the best interest of your general userbase, then that is of course your decision as it is your plugin. However, not including such an option is not going to convince me to include titles on each and every post. As I said, I would simply use the option to not display any titles at all. I might possibly take a screen shot of the titles on posts that have them to include as a thumbnail, but that is an extra step that I’d prefer not to waste time on.
Perhaps I should rethink the idea of even having a recent posts widget at all. It does seem to take up a fair amount of space on the side bar, even if I only limit it to three posts, though there may be other places on the website where it would be more appropriate.