I'm very much in favor of letting people be as expressive as they want with their levels, even if others may deem it as low quality. I feel removing certain levels should rarely happen unless a level is impossible, a direct copy of someone else's level, contains actual NSFW imagery in the skybox or level thumbnail (NSFW help text would be a grey area and would be at the discretion of how others perceive it) or contains any personally identifying info. That is basically my few guidelines on if a level should be removed or not, I'll delve more into the considerations you provided below:
Construction:
Everyone is free to build their levels however they want, even if that entails gem spam and random interior spam. We all have to start from somewhere when making levels, and some choose to start with gem/interior spam in the LE. It's very unfair to a new level builder if their level gets removed just because they are inexperienced and/or don't have access to Constructor or don't know how to use other level building software. If an established creator wants to create an unfunny meme level with random slop, they also should be free to do that. This would also extend to levels that mix different game assets with each other, and mix challenge scores with different game themes (ATs with a MBU/MBP/MBG theme).
Removing these would basically be saying "You are not allowed to have creative freedom with your level-building process, you must stick to following the design philosophies that all established creators implicitly follow." We currently don't remove these sorts of levels which is great, but I don't want a precedent to be set where we start removing levels based on people's different interpretations of slop, which could lead to some grey areas down the line. I'd rather keep the new level builders happy and not stressed out over whether their level will count as spam or not, and I will simply just not play the level if I don't like what I see initially. All the examples you posted would be given a thumbs-up from me to stay up based on this logic.
Like I said above, the only levels that should be removed with regards to construction are duplicate or impossible levels. Someone uploading another person's level without their permission is flat-out plagiarism as a general rule of thumb, but there certainly are edge cases in which it could be permissible to do so (archival purposes maybe). Impossible levels should usually be instantly removed too. What's the point of playing a level if you can't even finish it after all? I could see an edge case where someone uploads a really difficult puzzle level that we have to try and figure out, but hints at the very least need to be given to guide the player in the right direction.
Gameplay:
A lot of what I could say here I think I already covered in my construction segment. If I had to add any more to it though, there are a lot of levels out there that are more polished than just gem/interior spam, and people still consider them "Not worth playing" so moderating levels based on this will end very poorly and create unneeded double standards.
Level Preview/Icon:
This is a non-issue to me. These should be treated as a design preference more than anything, just like mixing interiors or mixing challenge times. The first example is pretty innocent, just a little kid showing off his dogs. Can't get more wholesome than that, even if it doesn't convey the level well it's still cute. If someone isn't interested in the level based on that, it is as simple as not playing it. Example 2 is a meme level, so I think all expectations of any good quality should be thrown out the window automatically. Example 3 is the most abysmal case of a misleading preview, but I'd much rather not see it removed because the actual level has nothing wrong with it. As I said with example 1, everyone has a choice to simply ignore the obvious bad quality levels. No one is forcing anyone to play slop if they don't want to.
Level previews are just another avenue to express your creativity. If someone doesn't want to use a traditionally good level preview, that is fine, no one should stop said person from doing so unless it has actual NSFW pictures, or it reveals someone's personal info. This would apply to the skybox and any textures the level has too. Puppydog's Therefore mod would be an example of breaking the "no personal info" guideline.