I won't be signing either, and I say that as a very pregnant person going for a c section this week.
I don't know yet whether my hospital allows partners for the birth still; last week the policy for c sections was that they could be with you for the op and a while after, then had to leave until a one hour visiting slot later in the day.
If the policy has changed and partners can't be there at all, then so be it. I am a grown adult and will manage. A policy of completely excluding birth parters would halve the number of people coming on to the labour/postnatal ward. That's a massive reduction that will drastically reduce the risk of the staff and mothers and babies picking up the virus in hospital.
I think all visitors to hospitals should be stopped now, with the exception of a single parent to accompany children. I am not yet at the point where I'd be ok with a policy that meant parents signing over consent to the hospital, and children can't consent for themselves. Young children are also likely to be highly traumatised by being left in a hospital alone, and would be a childcare nightmare for staff.
Grown women can manage alone if they have to. Not ideal, not what pregnant people are currently coached towards in the antenatal period, but completely possible if it is needed to protect other women and the staff that are needed to safely deliver labouring women.