So we agree that, on average, the block size will increase approximately 2x in Segwit. With that 2x size increase we will also get 2x throughput? If so, we could have done just as well simply increasing block size without Segwit.
No, that would have been reckless.
Segwit (amongst other fixes already mentioned) fixed a Denial of Service attack. That DoS attack was increasingly more effective as blocks became larger. This could have been used to force the Bitcoin network into long waits between blocks while CPUs struggled to process the attack blocks.
So, it wasn't safe to increase the size of blocks without mitigating the attack. Segwit constrained that attack, and increased the maximum block size at the same time.