I've always been a fan of leaving my children to play by themselves. Its not that I never join them on the floor, I do, but I've never been one to sit on the sofa just holding them or cuddling them for big long lengths of time - hours I mean - I just am one of those people who is up and down, up and down, always thinking of things I have to do and get done.
So I'd feed my baby, wind them and change them, have a little cuddle and a game, and then settle them on the floor, with some toys, and then go and potter around.
I was lucky in that they were never crying type babies, my 2nd one didn't even cry to feed. She can go days and days without crying. She's 9 months now.
Re the cot thing - yes, you can leave them when they wake in the morning or after they've woken from a nap if they are not crying and due a feed - if you just hear them chortling away to themselves, absolutely. This is how I have a shower in the morning - when I hear her babbling away I know she is awake so I get in the shower, as its always 15 or more minutes before she'd get impatient. My son was hungrier than her so I'd feed him, have a cuddle in bed, open all the curtains etc then pop him back in the cot with his mobile on. When he was older I tended to wait till the morning nap to have a shower but he was firstborn so I didn't have to go out before then therefore there was no reason to be ready for the day and dressed till later.
Encourage it! I always have and at 3, my son is very independent. We arrive at soft-play and he's gone, I dont see him for 3 hours! We are also very bonded - at the end of the day, when we are in for the evening and about to do dinner etc, he will sit on me for a cuddle and play with my hair and say cute things.
The two children are also very good at going off and playing together! And at 9 months, if they "need" you, they can "tell" you - my daughter will crawl up to me and pull up on my legs if she needs picking up and cuddling - which I love!
YANBU