Steps to reproduce the issue

Download Joomla 5.1 and unzip it
Do:
$ php installation/joomla.php help install

prompt say:

...
      --public-folder[=PUBLIC-FOLDER]                    Relative or absolute path to the public folder [default: ""]
...

so public-folder is optional

Do:

php installation/joomla.php install \
  --site-name="Joomla! Demo" \
  --admin-user="Joomla Demo" \
  --admin-username="Superuser" \
  --admin-password="MyPassword123456()" \
  --admin-email="demo@localhost.xx" \
  --db-type="mysqli" \
  --db-host="localhost" \
  --db-user="db_user" \
  --db-pass="db_pass" \
  --db-name="db_name" \
  --db-prefix="gtlzk_" \
  --db-encryption=0

Expected result

Joomla is instalated

Actual result

The CLI ask:

Install Joomla
==============

Checking system requirements...OK
Collecting configuration...

 Relative or absolute path to the public folder []:
 >

Additional comments

The option --public-folder must use the default value "" if is not specified