I can't fully agree with you because if you see the ranking of icc t20 you will see that India is on the Top position on it on the others hand Pakistan at the 3rd place . Even then India is taking 1st place but recently England is the strongest team from both side batting and bowling. And then if you talk about any strong team who are good in both batting and bowling sides then I will talk about India. And if I talk about Pakistan then their bowling side is good but the lack you are talking that is on their batting side.
India's advantage is that their player pool is so huge. They can send their 3rd or 4th string team, and still win matches against the top teams. And that is not the case with teams such as New Zealand. Some of the smaller test playing nations even have the same squad for different formats. England is the second best when we talk about player pool, partly due to their strong county system. But even their performance has gone down recently and are struggling to compete against teams such as India.