If you make it read-only, maybe. If anyone can generate a link, wait for your hosting provider to shout at you and ask why there is so much spam/illegal content with your domain. The you realize you can't actually manage a service like this.
I used to work for a company that ran our own. It required authentication to add a new URL, and only employees had that.
As we already have a PostgreSQL database server, thecost of running this is extremely low, and we aren't concerned about GDPR (etc) issues with using a third-party site.
dub.sh comes to my mind
I use pinboard.in. Also pay the $20/yr for archiving if the links rot