In recent history, every new AB of C has presided over a shrinking Church of England, so maybe it's time for a more creative selection system. Some alternatives:
Crown Disappointments Commission: works by process of elimination, removing every bishop who was sniffy about Charles marrying Camilla, did a boring sermon at a royal occasion, or made offhand remarks about the Royals on social media.
Just a Misquote: Each candidate has to give an interview to Ruth Gledhill without providing anything that can be turned into a front-page Times headline on a church split.
Hunger Games Style: Each Diocese offers two 'tributes' (known as the Diocesan and the Suffragan), who fight it out in a sealed arena, a gigantic booby-trapped theological library. The one who defeats all the others in theological argument is the winner. Part way through, just to spice it up, several rogue Deans and retired Bishops are released into the arena to take pot-shots at the contestants.
Episcopal Wipeout: can the brave competitors get across the Tippy Tables of Human Sexuality, making statements of support for marriage without fully endorsing a particular opinion? Watch them as they juggle the Big Red Balls of Scripture, Tradition, Reason and Experience and try not to drop one. Gasp as they face the Sweeper, trying to stand their ground in the face of repeated swipes from lobby groups.
Bishops Got Talent: each candidate has to preach to the BGT panel. The red button is hit for bad jokes, churchy jargon, generalisations, or when the judge falls asleep and slumps forward onto their desk.
Pardoners Question Time: Decide which is the most unforgivable sin: blessing gay marriage, not blessing gay marriage, changing authorised liturgy or recieving communion from a woman. As this is a radio show, it's not clear whether the sound in the background is applause or people slapping their foreheads.
Pagans Den: each candidate is locked into a Glastonbury pub for an overnight session, the one to emerge with the most converts wins. In the absence of converts, gift-aided donations to the Cathedral maintenance fund will be used as a tie-breaker.
Bish Brother: all the bishops are locked into Church House and voted out over several weeks by the rest of the Anglican Communion. This one has been shelved in the face of concerns that, without the bishops around, the CofE would actually get on fine, and not want to let the bishops out at all.
British Parliamentary Democracy: "I say Jeremy, just text Rupert and see which one he thinks we should appoint."
I'm sure the new chap in charge of choosing Rowans successor will value this contribution.