Is a Linux system without a root user possible?

Short answer: not really.

Practical answer: you can design operations so daily work does not require logging in as root. That is exactly the RootAsRole objective with Linux capabilities.

Example: preparing Apache management without root processes.

First, create the service account:

dosr adduser apache2

Then create a task to install Apache with that account:

dosr chsr r r_root t install_apache2 add
dosr chsr r r_root t install_apache2 cmd whitelist add /usr/sbin/apt install apache2
dosr chsr r r_root t install_apache2 cmd whitelist add "/usr/sbin/apt ^upgrade( -y)? apache2$"
dosr chsr r r_root t install_apache2 cred set --caps CAP_CHOWN,CAP_DAC_OVERRIDE,CAP_NET_BIND_SERVICE,CAP_SETUID --setuid apache2 --setgid apache2

Add another task to start/stop Apache:

dosr chsr r r_root t start_apache2 add
dosr chsr r r_root t start_apache2 cmd whitelist add "/usr/sbin/systemctl ^((re)?start|stop) apache2$"
dosr chsr r r_root t start_apache2 cmd whitelist add "/usr/bin/service ^apache2 ((re)?start|stop)$"
dosr chsr r r_root t install_apache2 cred set --caps CAP_NET_BIND_SERVICE,CAP_SETUID --setuid apache2 --setgid apache2

Now installation can be delegated through policy:

dosr apt install apache2

Then service control can also run through delegated tasks:

dosr systemctl start apache2