In general, it's always better to use semantic HTML tags like H1, H2, H3, etc., as they provide structure and accessibility to your content. However, I understand that in some cases, you may need more flexibility in terms of font sizes and styles.
If you decide to use a different system for typography specifications, make sure to clearly communicate it with your development team and provide them with detailed guidelines on how to implement it. It's also essential to test your design thoroughly across different devices and platforms to ensure that it's accessible and usable for all users.
In summary, while it's generally recommended to use semantic HTML tags, using a different typography system can be acceptable as long as you communicate it clearly and thoroughly to your development team and ensure that it's accessible and usable for all users.