Update (20 August 2021): There is no longer a $300 publication fee.
Deferred examination exists in the U.S. under 37 CFR 1.103(d) (up to three years) but there are no advantages regarding fees and there is a forfeiture of patent term/adjustment. The only advantage is delayed prosecution expenditures. If you want to slow down an application’s prosecution we can file a petition before a first office action issues. But, we do have to pay the publication fee ($300) and a petition fee ($130). One would eventually pay the $300 publication fee at issue anyway so perhaps there are circumstances in which you’d want to slow down prosecution for $130.
Delayed examination (aka “Track III”) never made it into the AIA as signed. However, Track III can probably be implemented by the USPTO without further legislation. Track III will allow the delay of payment of Search, Examination, Claims, and other surcharge fees for original 111(a) filings for up to 30 months.