Multiple instances of CI4 and removal of public/index.php/ from url

Yes, you can remove the public/ directory completely, but this will introduce security issues since all of the CodeIgniter files will be accessible from the web.
You can read on how you can set up multiple applications using a single instance of CI4, so that your directory structure could be like

system...
vendor...
writable...
public_html
     app1
     app2

Otherwise, if you want all files in your in the same directory as the index, you can create an index.php file in the root of your CI instance then paste the following code

PHP Code:

<?php

// Valid PHP Version?
$minPHPVersion = '7.2';
if (phpversion() < $minPHPVersion)
{
    die("Your PHP version must be {$minPHPVersion} or higher to run CodeIgniter. Current version: " . phpversion());
}
unset($minPHPVersion);

// Path to the front controller (this file)
define('FCPATH', __DIR__ . DIRECTORY_SEPARATOR);

// Location of the Paths config file.
// This is the line that might need to be changed, depending on your folder structure.
$pathsPath = FCPATH . 'app/Config/Paths.php';
// ^^^ Change this if you move your application folder

/*
 *---------------------------------------------------------------
 * BOOTSTRAP THE APPLICATION
 *---------------------------------------------------------------
 * This process sets up the path constants, loads and registers
 * our autoloader, along with Composer's, loads our constants
 * and fires up an environment-specific bootstrapping.
 */

// Ensure the current directory is pointing to the front controller's directory
chdir(__DIR__);

// Load our paths config file
require $pathsPath;
$paths = new Config\Paths();

// Location of the framework bootstrap file.
$app = require rtrim($paths->systemDirectory, '/ ') . '/bootstrap.php';

/*
 *---------------------------------------------------------------
 * LAUNCH THE APPLICATION
 *---------------------------------------------------------------
 * Now that everything is setup, it's time to actually fire
 * up the engines and make this app do its thang.
 */
$app->run();