> BN is used to reduce covariate shift, it just happened to regularize.

The first part was hypothesized, but not proven. It is a popular belief, like all other hypotheses why BN works so well.

> Dropout as a regularizing technique didn't become big before ResNet (2014 vs. 2015).

What does becoming big mean? Dropout was introduced in 2012 and used ever since. It was never big in the sense that you would always use it.

It is certainly false that Dropout was used because of ResNets or immediately after them for CNNs, as the first paper proving that there is benefit in using Dropout for convolutional layers was in 2017: https://link.springer.com/chapter/10.1007/978-3-319-54184-6_12

> I doubt what you're saying is true, that they're effectively the same.

I never said that.