Extending the kitchen cabinets instead of the desk is a good idea.

One-level islands give better counter space.

The morning room looks really tight, even in the pictures. I don't think it can accommodate a table unless you reduce the length of the island, and definitely not unless you eliminate seating on the short end of the island. Can you use the media room as a dining room? Then you can have a table and a longer island with more seating. You can put a TV in the great room or the living room.

I agree with Emily. You might include a command/communication center someplace in that extension of kitchen cabinets which is a place for a family calendar, schedules, invitations, a charging station, etc., if you don't have one elsewhere in the house but most people find they don't really use the desk much.

I think the morning room is just a glorified hallway. At 7-feet, there's barely room for a table there much less the chairs and space for people to sit at them. Once you put in a table, it will block access to the media room. 60" is needed between two seating areas to allow for the chairs, space for people to sit in those chairs at the same time, and room to walk between them. That only leaves you 24" for a table with no one sitting on the other side. I have no idea why an architect would even design something like that.

To illustrate - of course, this isn't to scale but I eye-ball measured in that 7' wide space and the table is only around 30" wide which is a very narrow table.