Competition will drive players to find better gear, better builds, and better ways to play more than any other changes they may make. RoS appears to be in great shape, but how long will it last? How long will players set personal goals?
Of course players have different tolerances for both competition and personal goals. Some players may get bored after a single play through, others will put in hundreds of hours to find a grail item (and then another). Diablo population is skewed very heavily towards the single play through type of players. Competition is varied from very casual (think LoL unranked), to extremely intense. Population in competitive games has a much more even distribution of players and a higher retention rate (You might be thinking, 'but what about Wow?' Besides its monstrous amount of content, competition is found at the very basic level of standing in town inspecting other players.)
I believe that competition is a much greater motivator than solo play and provides great highs (and some lows) that make it exciting.
A system for players to compete with themselves or with others would be huge for the longevity and community of Diablo 3.
One example:
Allow players to turn in rift keys in various quantities.
The number of rift keys turned in determines the number of rifts within rifts.
Each subsequent rift increases in difficulty.
There will be a ranking system for both number of rifts completed and the time in which they were completed.
Could have various achievements/rewards for completing rift(s) of a certain depth or time.