There is no p2p network. There are no full nodes and no SPV wallets. The entirety of the network is these dozen miners connected to each other basically forming one big server cluster.
Each miner provides paid "services" in addition to mining. These services will include an API for paid subscribers to query to see their balances and transaction history.
They will also have an API to send tx's.
Thus the only way non-miners will be able to interact with the network will be to pick one of these miners and buy services from them.
There is no need to bother with cryptographic proof that your transaction is valid because you can't validate your transactions anyway. SPV is worthless because there are only 12 nodes
which can trivially make up a header chain and feed it to you. So you just ask for your balance and they tell it to you and that's it.
Tx ordering is only a secondary use case for pow.
