Two small feature requests:-)
Being able to pin tabs like you can in most browsers. This will re-connect those tabs when you start Core Shell. You should also be able to pin the Hosts window. This will save me a lot of steps as I always tend to more or less re-open the same sessions every time.
Set a preference for default open mode. I always want to open sessions in a new tab. I have that on a right click in the Hosts window. It would save time and clicks to let a user set a default behavior.