Promoting Ideas to Features will populate the Feature system scorecard field with the idea scorecard values as long as both the Idea and Feature are using the same custom scorecard.
The desire is for the same behavior when promoting ideas to initiatives, however, the mechanics for how this is done are going to be different. What is different is that Initiatives don't have a built-in system scorecard. Rather, if you want to prioritize initiatives using scorecards, you need to add a scorecard custom field type to Initiatives. The desired behavior would be as long as the idea scorecard and the Initiative scorecard custom field are both using the same scorecard that the idea scorecard values would seamlessly transfer over to the initiative upon promotion.
The workaround at the present time to support having idea scorecard values be updated to initiative scorecard values upon promotion requires adding scorecard custom fields to both ideas and initiatives and ensuring both scorecard custom fields use the same custom scorecard and have the same key. While this works, it results in having both the idea system scorecard and an Idea custom scorecard which can be the source of confusion.
Initiatives now have a standard product value score field. If you configure your ideas and initiatives to use the same scorecard, then the score will copy over when you promote the idea.
I am having exactly this issue, and I am surprised this hasn't been resolved yet