There's no reason you cannot use an extension cord with UTH...& I've used many UTHs for many years. "They" do say that it's best not to use extension cords with
ANYTHING long-term, that they should be temporary use only...I don't know why that is though; I would speculate that it has more to do with the WAY many people
use extension cords, such as placing them where they get stepped on & damaged, or they use them with high-wattage appliances that cause the cords to heat up, &
in time they physically break down. UTH are fairly low-wattage, at least all the ones I've used are. That said, the use of a multi-outlet surge protector is a better idea.