It really depends on the participant, but generally speaking, say in the FX markets, hedge funds would buy options to get exposure to volatility, not the underlying, so they delta hedge the option. The banks desks dealing the options don’t want exposure to the underlying either as these would be volatility desks whose expertise is vol so they would delta hedge as well. Hence there is an automatic match, and you will get better terms than if you were to hedge delta with a new counterparty or as a new trade.
The delta hedge will be updated as the option delta changes but you will have to start somewhere, though possibly many participants would have a strategy to hedge only material exposure. but then you won’t own just one option.