This is the way Ordered features work in Solid Edge. If you want to keep a sketch after a feature is deleted, then you can perform the same process using two steps where you first create a Sketch on the face where you wish to create a feature then use the Extrude command but specify the "Select From Sketch" option on the Command Bar.
Alternatively, if you want to keep your inputs to features you want to remove, you can Suppress the feature instead of deleting it.
In which situation you create a feature and later you decide to delete that feature but wanted to keep the sketch?
One thing I do, is before I delete the feature, I edit the profile of the feature, copy sketch elements.
At this point i can delete the feature and paste the element inside a new feature.
If you look in the help menu you should find a topic talking about "feature modeling".
I think the issue revolves more around expected behavior due to experience with other CAD tools. In Solidworks, for example, the profile remains in the feature tree underneath the solid feature whereas in Solid Edge the profile is not a physical element in the feature tree. Therefore, when the feature is deleted in Works, the user has the option to delete the profile or keep it as a sketch feature. Solid Edge doesn't provide that option.
With an exposed profile in the feature tree, Works users can do more with existing profiles. Because Edge hides them, we cannot. Edge users have learned through experience to plan accordingly and create unique sketch features if elements within them will be reused. We have the "select from sketch" selection when creating profile geometry or we can "include" sketch elements into a profile. It's a different way to tackle the same problem.