Hello Mattea Cowell,
Thank you for posting this case in Microsoft Community!
Based on your description: New Outlook organizer can't accept new proposed time? I would like to cooperate with you working on this case. To clarify this case, as further research and investigation from my side, currently any meeting participants side could propose the new time when received the meeting invitation in New Outlook. But once proposed the new time, the meeting organizer will receive the response alert and could click Review proposed time to update and send the meeting invitation again. This is normal behaviour that there is no direct options or features to accept the new time without having to send an email back with the new time.

I understand your concerns here but please note Microsoft is constantly working on improving this product and adding more new features and the new Outlook for windows (Preview) version is still under active development. Therefore, I suggest keeping an eye on the Microsoft Outlook blog or the Microsoft 365 Roadmap | Microsoft 365 for any updates on this feature. In the meantime, I do apologize for the inconvenience this may cause and will also update here once I get additional information and the specific timeline for the feature improvement.
At this point, it is also recommended that click Help > Feedback or Contact support and provide feedback within the new Outlook for Windows and add your concern as an idea through the new Outlook in-app support Feedback site. Microsoft will keep monitoring customers feedback and valuable ideas there to consider/include in the future product update.
Please note that nobody here is the product developer/decision maker and has no control over the product. Everyone, including us as a community moderator, can only assist you with the query for providing available solutions and the feature's availability status within our scope and capability.
To check more details about how to submit feedback, kindly refer to this article Learn about how to provide feedback to Microsoft - Microsoft 365 admin | Microsoft Learn
Your understanding and patience will be appreciated. For other questions, feel free to add your post to the Microsoft Community.
Thank you!