WP cron will work just fine on our hosting. You can even trigger it by hand by just navigating to <your site>/wp-cron.php.
The only thing that will not work is having PHP code on your code trigger that wp-cron.php endpoint for you. Those requests will be blocked by this security system: Ensuring only web browsers can access your website
But again, this is not a problem for normal website functionality.
If the WordPress cron job queue is not being processed, that’s usually the result of some plugin adding broken jobs to the queue that are blocking the rest of the queue from being processed, or just adding such a large amount of jobs that WordPress is having trouble keeping up.
You can use a plugin like WP Crontrol to get more insight into the queue, and then try triggering the cron yourself with the wp-cron.php URL to see if you get get things moving.