I dont think the gets stick, he has done well with a Burnley side, but lets not forget he has relegations on his CV too - however I haven't seen much that qualifies him as a future EFC manager.
What has he done which makes him such a standout candidate?
Being genuine mate - if he goes to the final of a cup and gives it a go, or finishes where burnley are this season I will be impressed. However nothing he has done has overly impressed me, wins against big team - lots of clubs get gee'd up for that, it only matters though if its pushing you up the league.
IMO, he is Moyes 10 years ago, building a atmosphere around a club which fits him well - his next move needs to be chosen carefully because the higher expectation and spotlight might see him burn up like Moyes did at UTD.