It would be nice to remount as rw the filesystem when rpi-update detects that both the partitions boot and root are mounted as read-only
I'm sorry, that is not standard behaviour for tools that write files.
I worry that someone who has deliberately mounted boot read only would not be happy if I circumvented that.
Filesystems in readonly seems mandatory for production systems where there is no guarantee at all that the OS is switched off in a cleaner way. My experience is that, without the read-only way after several reboot the sd falls in a corrupted state and I have to re-flash it from scratch.
To some extent rpi-update behaves as apt-get, the latter hasn't got the option I requested but there is a simple way to achieve it see https://wiki.debian.org/ReadonlyRoot#Make_apt-get_remount_.2F_if_needed