It's getting to the point where I'd say we should just flat-out prohibit reelection to the same office for all federal positions, period.
It's not democracy's fault that voters are apathetic. What are you doing to shorten representation periods? Do you campaign against the incumbent regardless of who s/he is?
Imagine what a sitting president could do to keep their position for another term. Any number of executive orders, picking a fight to start a war, etc. We definitely don't need that and term limits help to prevent it.
A prime minister is vastly more powerful than a president. A PM has no checks or balances on his/her power, save perhaps the judiciary, but even then it's not much of a check. So long as he/she has party support, elections can be postponed indefinitely, laws can be enacted that modify voting procedures and rights, electorates can be redrawn to favour party members. The possibilities are nearly endless.
But we've yet to see a first-world PM become a tyrant, despite Oz and British PMs regularly serving more than 8 years. Why not? Because the people get bored and vote them out eventually. Good ones stay, the bad ones get the boot after a few years. It's the way things work.