Having everything matching is a dated look so updating to a bed head sounds a great idea. Is someone in then family handy with tools? You could remove the existing bed head and replace with an upholstered one.

Do you need underbed storage?

not necessarily Kate.

Most mattresses these days are designed to sit on a timber slat base. These bases can come looking like an ensemble and be covered and sides padded or as a frame or with built in storage underneath as per your pictures.
Being able to see under the bed is like hanging a vanity - you can see more floor adding to feeling or spaciousness which is important in a small room but then often end up with things stored underneath and dust collects. It does improve airflow to keep mattress healthier.
At the end of day it is up to you to decide on your preferred look and functionality.
Same with bed head.

Kate, great comments as usual, thanks :)