Mark Waugh averaged 45 in Test and 80 in ODI in 2001. In 2002 he was given 7 matches in both formats before being dropped. He averaged 86 in the Ashes so you aren't going to drop him for at least 2 series. That brings us to the return leg in SA where he averaged 34. Could have been dropped here, but they stuck with him with the 50 he made in the 1st test not to mention we didn't lose the series. Selectors had enough after his poor series in Pakistan. ODI wise he averaged 108 in the Tri series and 138 against India. 2 series later he was dropped, so I don't see how he was carried any longer in the ODI form, Test they carried him 1 series too many.
Mark Waugh being axed from ODIs was indeed a dreadful decision but I'm purely talking about Test selections here.
The last time Mark Waugh batted well in Tests was The Ashes. I'm not suggesting anyone kept him too long, because someone who's been a good, solid Test batsman for 11 years as Mark Waugh was deserves some grace. But truly ruthless selectors would've dropped him before they did. Instead they acted as most selectors do, and waited for quite a while.
Onto Ian Healy, he averaged 49 and 31 against Pakistan and during the Ashes. Remembering that Gilchrist hadn't yet changed the way we pick our keepers. He was basically dropped 2 series later the Zimbabwe game was pretty much a nothing game. So again I don't see Healy being carried any longer than he should have been and the selectors didn't let a fairy tale farewell get in the way.
Healy batted terribly in The Ashes 1998/99 (forget his series average, the only score of note he made was in the opening innings where he was dropped 3 times), terribly in West Indies in 1999 and terribly in the 1999/2000 tour to Sri Lanka and Zimbabwe. He too had been a fine wicketkeeper-batsman for a fair while (1993 to the Pakistan tour of 1998/99 in fact - he averaged 35 with the bat in that time) so he deserved some grace, but ruthless selectors would've ditched him for Gilchrist long before.
Gilchrist didn't change the way wicketkeepers were picked BTW, for Australia or anyone else - Australia had picked Rodney Marsh and Wayne Phillips (not to mention Tim Zoehrer) based on batting in the 1970s and 1980s. It's always been the way - it's basic sensible selection that a good-to-decent wicketkeeper who bats well adds infinitely more to a side than an outstanding wicketkeeper who doesn't bat or isn't much of a batsman.
Steve Waugh averaged 80 against SA in 2000, next series averaged 20. Then in 2001 he averaged 48 in the Carlton Series, 23 against India, 100 in the Natwest series before being dropped after the VB Series averaging 31. He was the captain of the side, averaged 100 the series before and the selectors sacked him. That was the ruthlessness I was referring to. As for him staying in the setup, well why shouldn't he have been kept in the setup when he averaged 107 in the Ashes 01. Yes he was given more leeway than Mark but that always happens with the captain. He repaid the faith in the series against Pakistan and from there on the rest is history.
I'm not saying Stephen Waugh didn't deserve the faith shown in him in the Test team, just that some ruthless selection would've seen him ditched. Instead leniency was shown and Waugh repaid it.
As for his being axed from ODIs, like his twin that wasn't ruthless, it was plain stupid. But not what I was referring to here.
As for Shane Warne 3 years of period of doing nothing, I'm assuming you mean his period between 1998 and 2001. He had 3 shockers in the Border-Gavaskar Trophy but other than that he performed like his normal self with 8 wickets at 14 against SL in 98 after being dropped, 12 wickets at 30 against Pakistan in 99, 15 wickets at 27 against NZ in 2000, and 31 wickets at 18 in the Ashes. So if that is a period of doing nothing then every bowler should be dropped. Yes he could have gone better against India but that was him only blimp in that period (having already been dropped for his poor showing in West Indies).
I realise the overall figures against teams other than India look decent (obviously still far below his standards of 1993-1998 and 2001-2005, in both periods in which he averaged 22). But the reality is the only time he bowled well between the Border-Gavaskar Trophies of 1997/98 and 2000/01 was in Sri Lanka in 1999/2000. I CBA going through every Test but I'll say that if you look at what happened in each game individually you'll struggle to find a single instance of his bowling well outside said Sri Lanka tour. And I don't mean getting good figures - I mean bowling well.
Fortunately the selectors realised that even despite this sustained paucity (so bad that there was genuine, well-founded speculation he intended to retire after the 2001 Ashes) he retained the potential to come out the other side, so instead of being harsh they were very, very lenient. And Warne (like Stephen Waugh) rewarded their leniency.