Please provide some expert commentary to the aborted flight of the German chancellor
Satellite phones would be for passenger use.  Over land, ATC uses VHF/UHF radio, and over sea, ATC uses HF radio or (text-based) satellite data links.

Based solely on the quotes in the question, it sounds like a power distribution panel in the aircraft failed, leaving them with no radios.  There are procedures for aircraft with failed radios to continue flight, but it's a lot of extra work for both the flight crew and ATC.  And who knows what other equipment on the same power panel was affected.

Having a satellite phone available means the crew may be able to contact ATC and arrange a diversion and landing faster and more easily than the usual no-radio (NORDO) procedures allow, but neither ATC nor the crew would want to operate that way for any longer than necessary to land safely.

Also, specific to a Head of State, the protection detail would want to reassure their comrades on the ground that the aircraft hasn't been attacked or hijacked, and they would also prefer any problems be repaired at home by people they've already vetted to reduce the risk of espionage or sabotage.