poisonborz noted in the forums that the Nextcloud/Apache conifg can be tweaked to rewrite the address bar URL that the user sees (and remove the index.php). As suggested/requested, we should add this by default for the v16.1 release IMO.
To repeat the steps required as script:
cd /var/www/nextcloud
echo "'htaccess.RewriteBase' => '/'" >> config.php
chown www-data .htaccess
runuser -u www-data php occ maintenance:update:htaccess
chown root .htaccess
systemctl restart apache2
FWIW, this requires mod_rewrite and mod_env (both enabled in the Nextcloud build code by default).