Should all military engineers consolidate into a separate branch under a Military Corps of Engineers?

I don't think that's how Title 10 works. The services are responsible for recruiting, retaining, equipping and administering their own service members. There's joint training all over military engineering, but I know of no other "career field" that is jointly managed by one service for all others.

Nope. We still need to be part of our respective Services. What a Seabee, Red Horse or Army Engineer does is not the same and they should trained to deal with the problems that arise in their Service. I believe it would diminish the ties that bind us to the job of supporting our Service.

I did 7 years as a Divisional Combat Engineer during the period when the strength of the Engineering went from a Battalion per Division to a Battalion per Brigade. When I started, a Combat Engineer Platoon Leader doubled as a Special Staff Member as the Task Force Engineer. When I left, the Battalion Commander was the Brigade Engineer, although the day to day planning was done by the Assistant Brigade Engineer and the S3. I served as a Platoon Leader/Task Force Engineer, Company Commander, S1 and ABE. If there is one weakness in the training of Engineer Officers, it is that most are not as tactically proficient as their Combat Arms counterparts.. I don't see putting another command in the loop as being a benefit.

Bad idea for organization. While we are joint at the higher strategic levels, the military still focuses on branch operations at the operational and tactical level. Each branch still has its own aviation, transportation and other positions.