Windows Phone DOES have an export to SIM feature. My Lumia 920 has it. I have found out that export to SIM is being turned off by a lot of carriers for whatever reason.
Where exactly do you find this 'export to SIM' feature? It isnt under settings with people. I have multiple accounts and only some of them are syncing to the live.com site so I need to back up all the ones on my phone
If the option is available on your phone, it would be found in the People Settings.

Since you don't see the option there, your phone doesn't provide the option and you won't be able to export the phone contacts to the SIM card.
This feature was not available on my Lumia 520 and Amazon, who I bought the phone from, said it was a fault. In addition the power switch failed again which meant I'd no way of getting my contacts onto an older phone whilst it would have been away getting
repaired. Amazon refunded me and I was able to buy a new phone, a Samsung on Android... I've owned Nokia's from 2000 and after all the hassle with the transfer, then denouement of Symbian and the takeover by Windows I've now made the right choice.