lurcher - that is exactly what happened with DS.
DD we delayed clamping (St Thomas', London) - no issues.
DS we also delayed clamping (US hospital) - done without question. He was a good healthy weight, and we went home the next day. At his first pediatrician's app though (5 days old) they suspected jaundice, ran a blood test and sent us straight to the ER where he was admitted.
He'd lost almost 10% body weight and needed phototherapy for 24hrs. He was totally fine afterwards (and put the weight on very quickly) so no long-term harm, but obviously an overnight stay in the hospital wasn't what we wanted.
We were later told that his red blood cell count at birth (not sure if they monitor this in the UK?) was sky-high due to leaving the cord to pulsate. His body wasn't able to deal with the huge amount of extra blood and so he developed jaundice.
I'm still pretty angry that nobody mentioned this to us as a possible complication: no doctor, midwife or doula in either pregnancy. Not sure it would have changed our choices, but we'd have been on the look-out for jaundice and maybe stayed the extra night in hospital immediately after birth to be sure he wasn't developing it.
As an aside, I was under a lot of pressure to FF once he was admitted (since, as I said, he needed a lot of fluid). I'd BF DD for 12m so was confident in how to feed and in my body's ability to make milk so resisted them, but a first time mother or someone less confident in BF may well have agreed and never established feeding. As it was I spent most of those 24hrs either offering the breast or hooked up to a pump...
So there are benefits, but also complications.