The question of succession in my opinion was the single most difficult and dangerous problem of the empire. I suppose it is such for any empire, but it seems as if it was especially so for the Romans.
The Tetrarchy was one of those nice ideas that looks good on paper, but upon implementation ancient human nature just could not come to terms with it. Eventually (particularly if there is not even a family connection), every Caesar will fancy himself an Augustus, and every Augustus an Augustus Caesar of the entire empire. 'For centuries before they had been slugging it out for the ultimate prize' they thought, 'so why should we abandon it now, I am best and I will take it.' Also there was an imbalance in the resources of the districts. Some had better men, others better money, the truth was the entire empire needed the entire empire to run effectively. Britannia needed the money of Syria, and Syria needed the manpower of Hispania.
I think perhaps the system could have worked if it were instituted during Pax Romana perhaps. It would have to have a long running precedence before people would take it for a good idea and a natural order of things.