I've done some tarp camping, and a lot of "cowboy camping" --- no tent or tarp, sleeping under the stars in climates/environments where I'm pretty sure there's not going to be rain or significant dew.

I think all of the comments made so far are right on the mark. I would add that I consider a tarp to be a situational thing. There are trails and times/seasons on those trails where I like the tarp (or poncho tarp) option. More often, where I live, I want an enclosed tent. It's not about mice or rats or snakes or the like, it's about the insect kingdom, and primarily various flying insects. And indeed sometimes wind, though if you know the prevailing wind (which can shift in the night ...) a tarp can be staked out well to deal with that. A PITA in the dark of night, however, to realize that you want to adjust or just put up in the first place a tarp to block wind.

One issue with tent vs. tarp that I don't think has been said is the fact that an enclosed tent is a bit warmer. I've camped in snow with a tarp, and don't say that you should bring a tent as a way to stay warm (!) but it is one of many factors in picking the various bits of gear that make up your sleep system.

Okay, and one final one: animals DO act differently to enclosed tents. I recall on overnight trip tarp camping in snow with some friends; the next morning we decided to leave gear and do a day hike before heading home. I had taken down my tarp and collapsed my trench, just put all of my stuff in a yard waste type of bag. My friends left their tents up. On return from the day hike, a fox had torn into my plastic bag and spread my stuff all around with minor damage, whereas the tents were untouched. Often animals do see a fully enclosed tent as a tangible object. This rarely means anything IMO, so put it in context, but ... I guess "non-zero" if you're listing factors.