Please correct me if you think my reasoning is not correct or you have more information.

I think the reason is on Page 14 of the White Paper:

https://smt.steem.io/smt-whitepaper.pdf

SMT creation fee
Issuing a smt_create_operation requires payment of smt_creation_fee. The amount
required is set by the smt_creation_fee field of dynamic_global_properties_object.
This field may contain a value in STEEM or SBD. If specified in SBD, an equivalent
amount of STEEM will be accepted, at the current price feed.
Initially, smt_creation_fee will be set to 1 SBD, and no means will be provided
to update it. Updates to the smt_creation_fee amount may occur in future hardforks,
however, so user-agents should read the smt_creation_fee value from the
dynamic_global_properties_object. User-agents should not assume the fee will
always be 1 SBD and they should be prepared to charge a separate fee paid to the
user-agent if the aim of the interface is to enable only a curated set of tokens.
The fee is destroyed by sending it to STEEM_NULL_ACCOUNT.

So how come that a SBD now is worth 13 USD?

The market speculates that there will be a huge demand for SBD because of Smart Media Token creations. Initially the price will be 1 SBD, but what if Steem gets overwhelmed by requests for SMT creations and the fee rises to 10,000 SBD?

The amount of SBD cannot be created out of thin air, only through posts. And many SBD holders might choose not to sell their SBDs only for 1 USD. If you cannot by sufficient SBDs, you will not be able to do the ICO of your SBD. There are less than 4,000,000 SBD available and the amount of SBD available will through SMT creation as well shrink, as they will be destroyed.

This creates scarcity and the result is rising prices.

This is what I think is going on. As always this is only my opinion and no investment advice.