My guess is it happens in all the sports.I follow tennis intensely, and questions in discussion boards as to how a player would have done in a certain era come up all the time (for example if Nadal would have won 2 Wimbledons if he were playing on the fast-grass, big-serving era of the 90s etc.).
Obviously in the current era (almost since 2003) the presence of a truly great attack is virtually non-existent, so in that sense, a batsman being great against such an attack is not of much use for the team. But what I have observed is, batsmen who consistently dominate under tough conditions (like against a peak Marshall, Lillee on a seaming wicket etc.) generally don't have much trouble dominating on flat-tracks against modest attacks.
If I were a team selector or a captain or fan of a team in the current era, I couldn't care less about how a certain player in the team would perform against great attacks of the past. All I would be bothered about is, if he can deliver the goods in the present situation.
But the point of labelling someone as an ATG or bestwoing greatness is completely different. It is quite honestly one's own opinion. It is very hard to find any absolute here. For me, it is very hard to consider a batsman with a severe weakness against pace or short pitched bowling as an all time great (no matter what era it is, or what the statistical acheivements of the batsman in that particular era are). I am much more compromising on weakness against spin.
Ideally I would expect someone who is considered an ATG to have at least one stellar series performance, playing his natural game, in all extremes. This would show that he is capable of performing well in any era (condition). But then, that is just my opinion/taste.
It really depends on one's viewing experience of cricket. As I have said before, those who have never seen Aus-Windies or England-Windies matches during the 80s would have no clue about the degree of difficulty a batsman had to face. Even watching India-RSA or Pak-RSA series in the mid-90s would give some idea.
It depends a lot on what sort of back-up the ATG bowlers have, and if in that series the back-up bowlers themselves were bowling like ATGs. According to many, Thommo was no ATG but the way he bowled at his peak (72 to mid-78), batsmen did not prefer facing him to Lillee (who is obviously an ATG).
Jason Gillespie was pretty ordinary in the absence of McGrath (ignoring his great performances against Zim/BD). But he was very very good as a back-up for McGrath.
Weathering the initial storm (of say the Windies attack of 80s) without giving away the wicket itself was a big deal. Occasionally batsmen truly did not have any respite. After the massacre at MCG in 1988, Allan Border retorted "
You wonder where your next single is going to come.". And this despite having a very good, tough batting line-up.
If you are suggesting that great batsmen of this era (with their attacking mindset and strokeplay, and positive attitude) would have done just as well against great attacks of the past (70s, 80s, 90s) by targetting the lesser bowlers, it is very hard to say.
One thing that works against your suggestion though is that performances of many great batsmen of this decade are not all too flattering when they came up against truly great attacks in adverse batting conditions like in the 90s to early 2000s.
To be fair to the batsmen of this era, it is true for batsmen of any era. There is some truth in Andy Robert's statement that all batsmen, no matter how great,are very vulnerable against ferocious pace. It is just that batsmen of this era are damn lucky while those of the 80s facing the Windies weren't that lucky
.
Nevertheless, it is hard to generalize one way or the other regarding batsmen of the current era. IMO, stats of all current batsmen would suffer if they had to play great attacks frequently. How much they suffer depends on how quickly and
how well batsmen of the current era adapt, and how strong their fundamentals of the game are.
