You don't need a hack. Just do a regular override in your template

you can take a look here:
https://www.j-over.de/en/overrides/mod_login/login-module-without-links.html
https://www.j-over.de/en/overrides/com_users/login-component-without-links.html

Where i have documented the needed things about the overrides. (wich is not a hack ;))

Maybe I wasn´t clear here. I´m not searching for a way to hide the visible appearance from the links. I´m searching for a way to BLOCK this feature so that a bot isn´t able to put in random email addresses or usernames. Removing the visual appearance from the links will not help here :). The issue is that on some of my joomla installations the users got a VERY large amount of "do you wish to reset your password" emails due to the reason that some spam bots try multiple email address combinations into the fields.

The only way to stop that is to remove this feature :)

Even if a bot tries a large number of times to guess an email address there is nothing in Joomla core that will send out a "do you wish to reset your password" email

I am closing this as the main issue reported being

on some of my joomla installations the users got a VERY large amount of "do you wish to reset your password" emails due to the reason that some spam bots try multiple email address combinations into the fields.
and as stated there is nothing in the joomla core that will do this