First, its pitiful comparing Hayden to Tendulkar......Hayden has a long way to go before he can match Tendulkar or Lara overall.
Anyways, as per your query, i think Australia would GLADLY keep Hayden or Tendy on current form for oh-about another year ?
Care to tell me what AUS did when Mark Taylor was having a rough patch ? Persisted with him!
Care to tell me what AUS did with Steve Waugh when he was going through a rough patch ? Persisted with him!
This is Taylor and Waugh's record during their 'lean patch':
Taylor

96-early 98)
Matches: 21
Innings: 36
Not Outs: 4
Total Runs: 941
Average: 29.40
HS: 129
C: 2
F: 3
% of innings with 50+ scores: 13.88
Steve Waugh: (late 2001- mid 2003)
Matches: 18
Innings: 25
Not Outs: 1
Total Runs: 778
Average: 32.41
HS: 103*
C:2
F: 4
% of innings with 50+ scores: 24.00%
# of double figure scores:
Contrast that to Tendulkar's record:
Matches: 15
Innings: 26
Not outs:3
Total Runs: 1044
Average: 45.39
HS: 241*
C: 3
F: 4
% of innings with 50+ scores: 26.92%
Even in his 'slump', he has what is considered a very good average ( typically defined as 40+) and is more consistent than Waugh or Taylor during their rough times......
So i dont know where you get the
MYTH that Australia chops their stars when they dont fire instead of doing what every other team does: give them time to work their way out of the slump.