No, they shouldn’t because even in vehicle to vehicle collisions SUVs kill 4 times more people than cars. Source
The people that have a legitimate use for such trucks should be required to apply for a exception and/or have a CDL.
Because in fact almost no one actually needs those trucks. Source [1]
Most people can use a trailer or rent a truck for the 1-2 times per year they need it.
[1] I work at a hardware store, specifically in the construction materials department. In 2 years of working there I had literally 1 person use their truck bed to haul a pallet of concrete bags, everyone else either used vans or a trailer. And just 2 weeks ago I had the first customer that used a pickup truck (Mercedes X-Class) to tow a 2.5t trailer to transport paving slabs.
So no, even trades people don’t need those trucks, so why the fuck should a normal “civilian” have those and be 4 times as likely to kill someone??
Get a safety razor. I got one a few years ago and it’s been amazing. The blades are much sharper (or at least feel that way) than the modern 4/5/6 bladed thingies, last longer, and are like 20€ for a 50-pack.