The arguments for inverter-driven units have been made again and again and are now completely accepted. Back in the old days, the old timers argued against them at every turn. Most of the arguments stemmed from the fact that bad engineers couldn't fix them and were scared to death by the electronic witch craft. To win over these flat Earthers, some manufacturers even introduced fixed speed units which actually had inverters in them set to run at one speed.
Unfortunately, the renewable heat sector is a long way behind and the inverter/non-inverter argument is back.
The problem is simple - in the last few years mass-market air source heat pumps have been developed using existing air conditioning technology including inverters. As recently as five years ago, heat pumps were made to order in sheds using ancient technologies. The old tin bashers making these things have never used inverters. They still produce hideous units complete with all manner of bits of metal to get around the fundamental problems associated with single speed units.
In a last ditch attempt to keep producing these ancient contraptions, some of these people have decided to attack this technology with spurious and ill-informed arguments. I recently saw an article by a manufacturer claiming a tissue of lies about inverter-driven units. Some of the claims were practically libellous - the units are dangerous, they offer lower efficiencies, they are more unreliable, too complicated etc.
Ned Ludd would be proud.