Removing the like button for all users on the site seems like it would be fairly straightforward, but would require a lot of customization to the site’s layout. These types of customizations can break Discourse if the base layout gets changed in a Discourse update.
Only removing the like functionality for some users, so that they could neither like posts or have their posts liked seems like it would be a difficult project.
My own opinion is that likes are beneficial to Discourse. They are a simple way of exchanging attention. They also help to reduce noise in a topic by reducing the number of “thanks” types of posts. One thing to note about likes is that you are the owner of your Discourse site, so some of the social engineering concerns about the use of likes on major social media platforms might not apply to your Discourse site. I’m sure you’re not trying to addict users to the site so that you can collect as much of their personal data as possible.
One setting that your users should be aware of is the “Notify when liked” setting that is found in the Notifications setting of the user’s profile page. That setting defaults to “First time a post is liked and daily.” Some users on your site might prefer to set it to “First time a post is liked”, or “Never.” If you find that you’re getting too many notifications from a Discourse site, this setting is a great way to reduce them.