Why is the root file system mounted read-only during boot and remounted with write permission...

Because if problems with the root file system are detected during the boot, fsck can be run, without risk of damage.

Because this way crackers cannot collect information about root with boot sniffers.

To avoid writing to the disk, unless the root password is known.

To avoid other operating systems overwriting the Linux root partition.

Because the disk has its own write protection that cannot be changed by the operating system.