Nope. It's not true. They're beautiful, and you will find folks singing their praises-- they're elegant like a wooden canoe, or a cedar strip kayak
Sometimes, the Ancients design the perfect piece of gear that cannot be improved upon. Traditional snowshoes are an exquisite functional thing of beauty, and they are NOTold fashioned. They are still by far the best choice for many snow conditions and trekking styles. They are light, provide excellent floatation, pack a “float” trail for a sled, and shed snow on the up-step. But there is such a wide variety of designs, shapes and sizes, that it can be a bewildering choice.
-- but at the cost of taking some of the romance out of the world, they just don't perform as well.
Modern snowshoes are lighter and stronger, require little to no maintenance; snowshoeing is exhausting hard work, and a lightweight modern snowshoe is vastly more capable. There are a bunch of snowshoe races in all kinds of terrain and conditions-- I'm not aware of any winner wearing traditional snowshoes. Someone's probably tried it, but just like no one is doing Giant Slalom on wooden skis, you're not going to see a lot of the traditional snowshoes in anything competitive.
If you want to go long distances in deep powdery dry snow, you'll do OK with traditional designs. Where I live -- the Columbia Gorge-- we get a lot of icy conditions over snow, and a modern snowshoe with metal crampons and a serrated frame for added "bite" is a necessity as you traverse steep icy slopes. Traditional wood and rawhide snowshoes don't do well in the wet heavy snow of the Pacific Northwest-- you'll find everything getting soaked through, heavy, and collecting ice.
Consider the contrast between early 20th century wood tennis rackets strung with catgut and modern graphite frames, or between wooden skis and leather ski boots, compared with ones made from advanced materials. The traditional designs were ingenious, made excellent use of available materials, but modern materials have unbeatable weight and strength properties.
Sources:
The Knights of the Snowshoe: A Study of the Evolution of Sport in Nineteenth Century Montreal
"Traditional Snowshoe Designs" on Winter Trekking dot com