I've been talking to Visa's tokenization team and several payments experts over the last few weeks about this exact topic. Currently, TSPs are only the card networks. In the future, the big banks and the payment processors will also take on TSP responsibility. It is unlikely that other actors will take on this role, given the requirements and players involved. The role that's more likely to allow for innovation is the Token Requestor role - which virtual wallet providers and e-commerce merchant / merchant processors can play a part. Even this role will require a decent amount of scrutiny in terms of the ability to identify the validity of a transaction, which is ranked on a 0-99 scale. Very interesting future for payments.

It's both. Issuing banks can generate the payment tokens, but often, the networks can "stand-in" for the issuer, and generate the token for them on their behalf (the same way that networks can stand-in and do authorization of payments on behalf of the issuer).