No (somewhat complicated question but that's really the answer).
Anyway, as a practical matter, at current or potentially even lower STEEM prices in the future, there isn't enough revenue for witnesses to do it. All witness rewards added together are only about $600K right now which is far less than what Steemit Inc. is spending on its node cluster. That is ALL witness revenue, and no it can't all be used to provide API nodes.
There needs to be a better business model that involves actual revenue to support the servers. Providing unlimited usage for free doesn't scale and isn't sustainable whether witnesses or Steemit Inc is doing it.
When steem was new (price=few cents), how witnesses were managing costs?
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Witness rewards were about 5x higher pre-HF16 as I noted elsewhere. Costs were also much lower (smaller blockchain), and the initial witnesses were all early adopter whales who didn't really need the rewards. In case you don't know power down used to take two years so the rewards (which have always been 100% SP) weren't even all that accessible to cover costs (plus for a while, no exchanges). Witnesses covered costs out of pocket, though again the costs were much lower (any cheap server would suffice).
Ok I didn't knew they had so many nodes
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@smooth drops mic :) booya!