It is really annoying to have two kinds of MGO (waves and ethereum chains) and they are not interchangeable in exchanges, unless you pay extra trading cost among various markets. Why don't the developers team do something for setting up an official site for 1-to-1 exchange of MGO acrossing two platforms? I think most people will happy to pay for the transfer cost (not cost of trading gap).
Is there any such site exist?

a tokenswap by the team is planned .. I think est was about 1 mtnh after release of the token .. correct me if I'm wrong.
That will not happen. Otherwise there's no point in dividing between two chains. I assume one of these will die out fast because of natural selection. Crowd wisdom has already shown that splits and hardforks such as ETC\ETH result in nothing but a series of damaging consequences that, I presume, will also happen here unless only one chain is chosen as primary.
k
https://mobilego.io/blockswap-will-mobilego-use/Advantages
Aside from allowing us to use the functionality of both blockchains, there are several advantages to employing BlockSwap for MobileGo. Crypto is still relatively fragmented, and this allows us to leverage interest and expertise from the Waves and Ethereum communities, as well as GAME. BlockSwap itself came about through a collaboration between two people building applications on Waves and Ethereum.
It also means that redundancy is built into the project. Should either blockchain become the target of an attack or a security vulnerability, tokens can still be safely hosted, transferred and traded on the other.
Lastly,
it increases the appeal of MobileGo for exchanges. If a given exchange has already integrated Waves or Ethereum tokens, this makes it easier to add MGO on either one of its supporting blockchains. Anyone can then deposit to the exchange to trade, either directly or using BlockSwap as an intermediary step and anyone who buys MGO from an exchange can withdraw it to the wallet of their choice.
You means this? It's not the truth, at least on exchanges listing .