Note I said "or" there. Decentralizing the infrastructure would make things cheaper and might give you revenue opportunity (and growth) that you wouldn't have otherwise. For example, perhaps you get into the business of aggregating ad sales to downstream providers.
As for directly monetizing the APIs, one thought that springs to mind is charging for the firehose in a federated way. You could, for example, have a query endpoint that looks like this to guarantee standard issuance of data, identity and payment:
GET /api/v1/status/access
{
"payment_address": "13kU1qPtM3WWXrNugWfRPNM1BniMQDw9Ds",
"rate_bytes_sec": 50000000,
"ask_expires_at": 1444492687,
"access_token": "h458Yf301",
"ask_in_satoshis": 1000000,
"ask_window_secs": 3600
}
Make a payment to the address, then start querying at 50MB/sec for the duration of your valid token (in this example, 2 hours):
GET /api/v1/status/h458Yf301
{
"payment_address": "13kU1qPtM3WWXrNugWfRPNM1BniMQDw9Ds",
"payment_received_address": "13kU1qPtM3WWXrNugWfRPNM1BniMQDw9Ds",
"payment_received": 2000000,
"access_expires_at": 1444499887,
"identity_screenname": "kordless",
"status_data_begins": [
]
}
And yes, I'm proposing Twitter should use Bitcoin to monetize query traffic. Even better, charge people for posting lots of statuses, or following and unfollowing lots of people. Link ask price to signal/noise ratio.