We share all the time. I like to go out to eat with my mother, because we've been doing Weight Watchers together for almost 6 months now so we're both equally aware of portion sizes and using our daily points wisely.
While there are some restaurants that offer great low cal meals (Applebees for example), for the most part portions are HUGE! Even when you think it's just a steak, you never know how it's been prepared. We have a member in our meeting who is a chef at Outback - he shared the unwelcome news that Outback complete coats each steak in real butter before it's cooked.

No wonder they're melt-in-your-mouth incredible! But the fat and calorie difference between that and a regular old steak you'd look up in a calorie counter book is massive. Diet or not - no one needs that much food, let alone that much saturated fat! Even with what appear to be good choices, you just never know what you're going to get. I tried to go the steak/veggies/baked potato route at Ruby Tuesday on my birthday, and I was quite happy with myself until I got home and checked the calories on their website.
So, we usually share out of necessity. Saturday afternoon we always do lunch at Panera, splitting either a turkey sandwich or an Asian sesame salad. If I had a whole sandwich to myself, it would easily take up more than half of my daily point allotment! We purchase an additional side, and they always offer to split the shared meal on to two plates.
Basically, we share anytime we look at the nutrition info and can't fit it into our daily points allotment. We always plan where we're eating in advance, and check the menus online before we go so that we have a good idea of the nutritional content before we get there with an empty stomach.

If I'm going out with someone that wants their own entree, I just eat half of mine and take the rest home. No problem, and I'm always plenty full afterwards.
Funny enough, my mother came along to WDW and we had
DDP, but we didn't share a single entree there. We usually shared an appetizer between 3 of us (we just didn't need 3 appetizers) and then ordered our own entrees and were just careful to stop when we were full - not when the plate was empty. We aimed for a lean cut of meat and good veggies, so the TS meals usually had the best options. Then we ordered our own desserts, and ate enough to feel satisfied but didn't finish those either. Again, it's just too much food.
I can absolutely see why people share meals at WDW and elsewhere - not to save money or meal credits, but certainly anyone watching their weight or just trying to make healthy eating choices. Everything in moderation! It's just really hard to find moderately sized meals in restaurants these days.