The operation of radio equipment worldwide is governed by the International Telecommunications Union (ITU). Implementation of the regulations is devolved to national governments who may further devolve responsibility. That ICAO deal specifically with aircraft systems.
Extracted from a summary of ICAO regulations;
"Simply stated, an airplane must be equipped with at least one operating hf radio capable of monitoring and communicating with air traffic control any time the airplane is operated beyond the range of ground-based vhf radio communication even if an operator has an operational SATCOMvoice or satellite Datalink system installed. ICAO Annex 2, Paragraph 3.6.5.1 directs this and also describes HF as a back-up to CPDLC. ICAO Annex 6 states this long-range communication directive again."
All documents are available as downloadable .pdf files from Google searches.
Due to the possibility of HF communications causing interference at extreme ranges, operators require some additional training and licensing in the use of such equipment. This is not the case where VHF and higher frequencies only are used.
The answer therefore is that it very much depends on where it is intended to operate an aircraft. Over Europe and Eastern Russia, continuous VHF coverage is a probibility. East of the Urals or into the Arctic, HF will be a requirement.