The screen is part of sterility - it is a barrier to the (usually) unmasked gasman and gasman assistant that hover at the head end for pain relief and life mainetence if required (hopefully not!)
That said it could be carefull wound down if someone wanted, alhtough it's mega tricky as the scrubbed people have a huge risk of breaking scrub by touching some non sterile bit of you or equipment and visa versa, and the non sterile people run a huge risk of touching some sterile bit of sheet. If this happens the whole op has to stop and everything changed - a amjor and poterntially challenging act.
In reference to the baby, they are basically at risk of bloody freezing in theatres. Our theatr is 24-25 degrees, and hotter and the scrubbed people start fainting. The baby comes out wet and in a large room with air flow (due to the nature of the air cleansing in theatres) which is a freezing combo. So the tendency is to dry and wrap wrap wrap. But certainly dry very very well.
Some trusts like a paed at delivery as all sorts of sections ( planned and otherwise) carry a risk to the newborn, they can be very likely to need oxygen in the firts 5 mins as they are not 'primed' to make the physiological adaptions needed i the first few mins. For this reason the paed or recieving midwife tend to want a really good look at them, observing for chest recession or nasal flaring etc whiklst they make sure they are 100% dry before wrapping in a million towels.
However, a well baby can be passed to mum and slid into skin to skin contact - just ask amile]
Some mums get very shaky or drouwsy in theatre also. And some plain freak. So this (I don't think) should be expercted of new mums in this situation. Same applies to partners, who I have seen do some very odd things!
Most I have asked have looked horrified at the notion of doing the skint o skin for the baby, only one has accepted - in 15 years!!
I'll never forget one dad who stood up and picked up an instrument for a look, midway through. We had to change everybit of drape, equipment and the surgeons had to rescrub. Not nice when your are lying there with your tummy open!! I can laugh about it now
Anyway, hope this helps. But yes, all activities have a ground 'reason' but lots can be worked around at request of lady 