Feels totally natural and right to me. But you must be aware of safety implications. Remember that modern beds, central heating, medication and bedding etc are NOT natural. There is much more scope for error when you bring a baby into a sleep space which was not designed for them. That said, it's always safer to co-sleep in a planned way than to accidentally fall asleep on a sofa or in a chair with a baby. If you're very very tired and can't stay awake, clear a space right in the middle of a double bed and lie down with the baby.
Don't co-sleep if anyone in the house smokes, or when you've drunk alcohol or taken medication which causes drowsiness. Smoking + co-sleeping doubles the risk of SIDS whereas just smoking alone doesn't increase it as dramatically.
Keep duvets, pillows etc away - most BF mums will naturally go into a "C" shape around the baby, if you don't do this naturally you should mimic it. You must be aware of where they are and take steps to stop them moving.
As close to skin to skin as possible is best, though light clothing is OK. Def no swaddles - affects their movement - or sleeping bags - not designed for a heat source (your body) on the outside. And no gadgets or items between you and the baby, this includes any sleep nests or pods or positioners the baby is lying on. Something like a muslin or bedwetting pad or electronic monitor under them is probably OK as minimal interference. Don't put them on top of the duvet, for the same reason (it is also too soft for them).
Make sure they can't fall out of bed, under another person in the bed or into any gaps. A bedside cot can be a godsend for this and also provide a safer own space for the baby to lie in which you can't roll into if you want more of a halfway house or to use products like a grobag, babynest etc. Make sure you follow the instructions for your bedside cot, you can usually download them if second hand, and check it regularly for gaps and movement.
Once you've got the safety awareness down I think it has massive benefits. Supports BF - DS never lost any of his birthweight and apparently this is pretty common when it comes to bedsharing. You can sleep (or doze, at least) while they feed which is hugely more resting, and means having to do all of the night feeds doesn't seem such a burden. The older they get the more likely you are to sleep totally through, whether they feed or not. At least until they get very wriggly.
I also found I worried less about his breathing and didn't do that new mum obsessively checking thing because I could feel/hear him right there next to me, so I didn't need to. I tended to be aware of things like his temperature and would wake up if he was ill, sometimes before he would. I did a little bit of EC at night when he was tiny and I found I'd even wake up to catch wees as well (In hindsight the whole EC thing was probably a bit bonkers, but anyway).
Babies seem to sleep better because they can safely be in the side lying position (if directly next to you) and they are comforted by your presence as it's all they have ever known. They don't go to sleep crying. They don't wake up crying. I know not all babies who sleep alone do this but I've never known of a co-sleeping baby who does. In fact DS used to frequently wake up with a beaming smile as though he couldn't imagine being anywhere better - there is no lovelier alarm clock! You don't have to sleep train if you feel rested and comfortable despite nighttime parenting.
I know it doesn't suit everyone, and lots of people find they sleep less soundly or have a lot of anxiety around it but for me personally it's the only thing that makes sense with a young baby.