How does US (its economy, banks, industry) profit from dollar being the "standard currency"? How does US (its economy, banks, industry, "finance industry") profit from dollar being the "standard currency"? I am not seeking "ideological" explanations, but explanations of the mechanisms involved, of the kind of "how things work", better backed by actual numbers. Could one recommend some honest, preferably not ideologically coloured, accessible reference which discusses such mechanisms?
Some major benefits include:


Seigniorage on currency acts as a source of government revenue, allowing for lower taxes and higher spending. One paper (Neumann (1992)) puts this at about \$15 billion a year. 
Lower borrowing costs on public and private debts due to greater demand for financial assets denominated in the currency, particularly credit risk-free assets. A McKinsey report (An exorbitant privilege? Implications of reserve currencies for competitiveness (2009)) estimates that this lowered the "...US borrowing rate by 50 to 60 basis points in recent years, generating a financial benefit of $90 billion".
Because households consume many non-tradable goods and services and earn income denominated in local currency, households naturally have hedges on the fluctuation of local currency. Increasing the scope of dollar denominated goods and assets increases the strength of this hedge, reducing currency risk in consumption, trade and finance. For example, Euro-ization is thought to have increased GDP on in the Eurozone by 0.4 percent per year (about 40 billion Euros) from the reduction of transaction and hedging costs (Emerson, Gros, Italianer, Pisani-Ferry, and Reichenbach(1992)). 
More liquid capital markets, because there are many more buyers and sellers of dollar denominated assets.
Deeper capital markets, because liquid and cheap capital encourages the raising of capital


You many also be interested in the book Exorbitant Privilege (Eichengreen (2012)) which includes an extensive discussion of this topic.