Is CTR really equally secure than CBC?
Your analysis is mostly correct, yet it ignores the reasons CBC has lost favour. CBC requires padding. And we have seen multiple practical attacks on the padding.

Nounce reuse in CTR is indeed much worse than IV reuse in CBC (which is bad enough).

I've seen implementation where the sender sends a full block length nonce(e.g 128 bit) and how he split it up is up to sender. receiver need not verify the bottom part starts with an appropriate number of trailing zeros. In fact the protocol could work even if we start each message with a fully random nonce with no trailing zeros and increment it.