I think it's pointless trying to emulate the setup of that side. The game has changed so much, there are loads of young batsmen like Lawrence and Pope who can match Pietersen for sheer audacity of stroke play because they've grown up on T20, the switch-hit is not an invention to them. Nowadays unless you can play multiple formats you find it difficult to play for a county, this combined with the fact the season is played mostly in April and September in overcast conditions it makes it very difficult to find batsmen who have scored runs or have any confidence in their skillset. I don't think England can find batsmen like Cook, Strauss and Trott because that's not what the game encourages anymore.
It's not an accident that England have a shitload of good all-rounders and wicket-keeper batsmen available and not many specialist batsmen or quick bowlers to call upon. There is also a strange fascination with orthodoxy within the English coaching structure which restricts natural talent from thriving, England could never have a Jasprit Bumrah for instance (although it remains to be seen if his action allows him to have a long test career).
Its not so much about emulating teams gone by but simply replacing quality with more quality. We've struggled to replace Sehwag, Gambhir and Laxman i.e. openers and a number 6 granted VVS may go down as one of the greatest lower order batsman there ever was. In Kohli, Pujara and Rahane we've almost attained like for like replacements for Tendulkar, Dravid and Ganguly - the first two just happened to be incredibly similar to their predecessors.
I'm not saying England need a run machine to replace Cook, a risk taker like Pietersen or a grafter like Trott. They need players to come in who can have the same impact but through different means. I said this before the series - Englands ODI rise has led to their test demise. Englands hard hitting batsmen struggled throught out the series due to their refusal to play the ball with soft hands.
Kohli demonstrated the ideal way to play in these conditions amd Cook went back in time to show us how he accumulated 12k runs - discipline, soft hands and intelligence. I see Olly Pope, albeit young, playing through the line in an aggressive manner and seeing himself being dropped - the ODI game doesnt work in these conditions. Its a completely different game. India win a few more close battles and this series could have been 4-1 against England. Thats not to say we don't have problems however, we've workes incredibly hard for 4 years to eradicate many of the issues with our bowling.
Overall, all International teams have major issues - some more so than others. England have a huge test coming up against two rubbish teams amd Herath in foreign conditions. India have a slightly less daunting task in Australia later this year. Both teams series' will tell us a little more about them and how much they've improved.
PS. KP wasnt just brilliant because of his stroke play - he was a run machine and had stats comparable to the little master for a little while. Had he carried on playing, he'd be Englands greatest, IMO.