Why is it so hard to make longer hashes?
That article is talking about the core function and state size. It's easy to get a larger output using a whole range of instructions. Using a counter, like your example, does indeed constitute a correct way of generating more output. It's extensively used in constructions for creating a pseudo random function (CSPRNG or DRBG) or key derivation function (KDF).

The problem is that if you want to also have 1024 / 512 bit security you'd need to use a larger state. In that case you'd need a different construct, or you'd have to use 128 bit instructions. Your example doesn't use a larger state and therefore is unlikely to provide full 1024 / 512 bit security. Currently however 128 / 256 bit security is deemed plenty, so there is very little reason to go that way.

If you want to have a hash function with the same security and still larger output, you might have a look at the SHA-3 XOF's: SHAKE-128 and SHAKE-256. Due to the construction of the sponge it's easy to generate more output while the internal state (and thus the security) remains the same. It's basically still SHA-3, it doesn't even need alteration of the core function nor an external construction using a counter.