It's not a graphics / framerate / resolution thing.
Single player can be 1080p 60 fps and look amazing. Split screen can be 720p, split into 2 and run at 25fps - one does not affect the other.
What split screen can do is affect the design of single player levels. In previous Halo games if you were playing co-op the 2 players had to be in the same area. You could never split the players up too far, so missions had to be designed with that limitation in mind. Otherwise you might end up with players constantly beaming to each other at really annoying moments.
In Halo 3 there's a mission where 3 teams split up and attack 3 separate towers. But in co-op both player must stick together and attack the same tower. In theory, now that Halo 5 has dropped split screen co-op, you could send 4 players to 4 separate locations across a vast area. Far bigger than anything seen in previous games without having to beam to each other.
If that's the reason they took out split screen co-op, then I'll look forward to playing Halo 5's new larger, more epic missions. And I'll keep hassling 343 to keep making improvements to the framerate on the split screen campaigns on the Master Chief Collection to get my couch co-op fix.
Seriously, if they continue to improve the Master Chief Collection and then add Reach at a later date, I'll have 6 Halo co-op campaigns to play with a buddy on my couch. At that point I can forgive Halo 5 dropping the feature.