Hello Jan,
Sorry to hear about this experience. Are you referring to CPU usage for Illustrator, similar to the screenshot below? If so, you may ignore this as Multiple CPUs (cores) and an app having multiple execution threads means each available CPU could be used in part or 100% for a sum in the Activity Monitor display greater than 100%.

Illustrator is a multi-threaded app, and you probably have a multi-core CPU, so this is normal behavior.
Also, you may try resetting Illustrator's preferences by following the steps shared in this article (https://helpx.adobe.com/illustrator/kb/troubleshoot-preference-issues.html) and sharing your observations.
Disclaimer: Please note that resetting preferences will remove all custom settings, and Illustrator will launch with the defaults. You may take a backup of these settings from the location mentioned in the article.
Looking forward to hearing from you.
Thanks,
Anubhav