There are definitely good bike options for carrying a load. Not trying to talk you out of a trike, but whats the main concern with some sort of cargo bike? Something like a radwagon would seem perfect for you.
The industry experts on trikes are Utah Trikes. They carry pretty much everything. I know you can't buy from them and get your rebate, but their website is a good place to browse and see whats available. Conventional trikes can be converted with a mid drive conversion kit with minor modifications. The Tongsheng TSDZ2 is popular for this (one of the few mid drive conversions that is torque sensing). Eco Cycles sells a trike conversion kit.
Note that trikes come in two configurations. Delta (one wheel in front, two in back) and tadpoles (two in front, one in back). Tadpoles are much more stable at speed. They tend to have a more recumbent riding position (laying more horizontal, like sitting in a recliner).
I think the main issue with trikes is that equivalent quality bikes are just waaaaay less expensive. Trikes are niche, low production items and just tend to be expensive.
I have a (non electric) trike i just want to know the diffrence between tricycle vs balance bike
. I inherited it from a friend who passed away. Its fun to ride. My main issue is its really unwieldy to carry around and transport, and mine is about as light and small as trikes get (2009 Catrike Speed). Trikes are physically large and tend to be heavier than a bike.