No need to stop. The XSS argument also applies when using cookies.
JWTs are just tokens like session data but in JSON format. What format you choose to go with doesn't matter.
You can keep storing JWTs in local storage and still be secure. Discord removes it on page load and restores it when the tab is closed.
Also if your website is susceptible to XSS, skill issue, exactly like in the case of SQL injections. That wouldn't have happened had people used the right tools and not played with fire.
JWTs are just tokens like session data but in JSON format. What format you choose to go with doesn't matter.
You can keep storing JWTs in local storage and still be secure. Discord removes it on page load and restores it when the tab is closed.
Also if your website is susceptible to XSS, skill issue, exactly like in the case of SQL injections. That wouldn't have happened had people used the right tools and not played with fire.