Supply down + Demand Up = higher prices.... not that hard.
Prices for nearly everything are going up. It has nothing to do with BEVs. It has to do with everything from lumber to microchips being in short supply.
Also... prices for used and new gasoline powered vehicles is going up too, so at worst, BEVs are just keeping pace with the industry as a whole.
Furthermore, no one gave a date as to when the cost of BEVs would dip below ICEs, so calling that misinformation is substantially premature. The big, experienced manufacturers like GM and MB have been awoken like a sleeping dragon and the new BEV platforms coming from them are going to be serious entries, not just an electric motor thrown in one of their gasser models with a bunch of laptop batteries in the trunk. As of about 3 years ago, they all started taking BEVs seriously.
There will be economies of scale as the cells of a Silverado don't need to be any different in composition than the cells in a Bolt... the only difference will be quantity. GM will no longer need to build 197 different powertrain combinations, it will be reduced to 10 (if memory serves, it's somewhere in that ballpark of a delta in powertrains). There will no longer be a need for complex 10-speed transmissions. No AWD systems. No exhaust systems. There won't be complex electro-mechanical systems to turn cylinders on and off while driving. There won't be turbo-chargers. There won't be those electronic shutters that close a grille at speed. All of that stuff listed that needs to be engineered and re-engineered every 5 - 7 years will go away.
None of that is in place today and no one claimed it would be in place by today, but you have the combined industrial might of GM, Ford, BMW, Mercedes, VW, Hyundai, Telsa, Panasonic, Samsung, LG, and others working on it.