Agreed on all points.
I do think that Ukraine is doing their best to mobilize, but it’s not easy. They are taking heavy losses, especially in the east. It mounts up, including in lost morale that makes it harder to get/keep new fighters.
It does seem that Ukraine is trying to move more forces out of the Donbass and south towards Kherson. That’s probably something they should have done before, in my opinion. Just to minimize the losses in the east, if no other reason.
The flat plain between Mykolaiv and Kherson is a potential killing field for anyone who tries to cross it, no doubt. Especially, as you said, without cover fire.
For me, this is all about the bridges (at least for now). Of course the fighting will continue in the east, with Russia grinding away, but all the key fighting currently is about bridges/river control.
To what degree is the fighting and disturbance of the nuclear plant affecting moves by either side?