Because if you read the research properly, you'll see it's just as safe (in fact some people believe safer) than cot sleeping. The research which tells us it is dangerous included sofa-sleeping, drunk/drugged sleeping, etc. Sofa-sharing is supposed to be the most dangerous. IT's infinitely more safe to set up a safe space to feed in bed than to accidentally fall asleep through tiredness while feeding on a sofa or in a chair.
Because you barely have to wake up to feed - I never knew how often DS was waking in the night. And you feed them, and then go back to sleep. You don't have to inch them into a cot. You don't have to walk down a cold hallway. You don't worry about "bad habits" with feeding to sleep. You don't have to listen to them crying, you tend to wake just before they do.
Because you are close to them, you can easily check their breathing, their temperature, you seem to know just before they are sick(!) you are just generally aware of how they are. This is one reason why I and some other people believe it's actually safer than cot sleeping. Also, if you sleep skin-to-skin, your skin temperature actually changes to correct theirs. Premature babies who have "kangaroo care" (skin to skin with mum)'s temperatures stay more stable (although mum's skin temperature will rapidly rise and fall by ~1C each way) than those in incubators (where the incubator has a steady temperature).
It's also beneficial, hormone-wise, for establishing breastfeeding. Babies who co-sleep and are allowed free access to the breast for the first few nights tend not to lose any weight, whereas a loss of up to 10% birthweight is accepted as normal.
When they go into a bed, they're already used to it, and you can continue settling them the way you always have, rather than having the sudden complication of it being changed (no sides). And people always seem to have trouble with cots - do you feed them to sleep and then try to get them in? Or put them in awake? Leave them to cry? What happens when they wake? You can't get in with them, so again you have the same dilemma. Often babies hate their cots or moses baskets at first - they just want to be with you. It seems the easiest and best solution for everyone.
I think most people who co-sleep are anti sleep training, as well. So the "obvious" solution to anyone who does think sleep training is good/necessary, isn't really an option.
It's also lovely to cuddle your baby all night, and wake up to them smiling and gurgling at you, and they don't tend to be wriggly and kicky when they've done it from being tiny.
I didn't kick XP out of bed. I don't see why that's necessary if you use a bedside cot or bed rail on mum's side. Unless they are a smoker, or something. I didn't really drink when DS was tiny but if I did have a drink I just made sure he was well inside the bounds of the bedside cot, and if he was feeding I sat up to make sure I didn't fall asleep on him.
Honestly I don't get why cots are so ubiquitous. I can't work out the logistics of them at all.