It really depends on just how far they plan on taking the split. If they are SERIOUSLY trying to have Raw and Smackdown compete with each other, both shows need a distinct 'top guy' that only crosses brands during the 4 major PPVs.
Lets say, for example, that RAW's top 4 guys are Roman Reigns, Seth Rollins, Dean Ambrose and Randy Orton. And let's say Roman is the champ.
Over on smackdown, the top 4 guys are maybe John Cena, AJ Styles, Sammy Zayne and Kevin Owens.
If SmackDown doesn't have a separate champ, You have to see Roman twice as often, rather than see SmackDown's top 4 guys being the main event. And if Cena ends up as the champ, the same thing happens to RAW.
If the rosters, writing and championships are TRULY split, you'd still have Roman highlighted on RAW and Cena (probably) highlighted on Smackdown, but the other 3 guys in each top 4 would also be getting more exposure on their respective shows. It basically doubles the number of top slots that talent can move into.
Having 1 champion would probably actually generate a lot of anger from the fans long term too. If the champ can go on both shows, but he's feuding with a RAW guy, it kind of makes anything that happens on SmackDown's top card not really matter.
If they are splitting the writers up by show as well, things can get really interesting. Right now the writers just play it safe, basically doing shit they already know Vince likes and taking few real risks. But if Vince goes into a RAW writers meeting and yells at them because SmackDown had higher ratings, those guys are going to be forced to try new things to keep the boss happy. Smackdown, from day 1, has a chance to become the A show and the writers will be acutely aware of that. I think they will be ready to take some risks immediately.
The only thing I think they are doing wrong is giving each brand their own PPV every month. On one hand, it could end up selling more Network subscriptions since you would be getting 2x the PPVs for $9.99/mo, but on the other hand, that's another 3+ hours a month of WWE product we'd have to get through. I think it could cause people to quit watching BOTH brands and only watch the one they prefer. And people not willing to get the Network are definitely not buying 2 $60 PPVs a month.