Why did the indigenous peoples of northern Asia and America not evolve the same physical characteristics as people of Nordic ancestry?

Why do Native Americans, East Asians, and circumpolar groups (i.e. Inuit) look so similar?

A lot of the reasons why Native Americans and east Asians look more similar is that they are more closely related, genetically speaking. Although there's been a lot of intermarriage between east Asian population and the rest of the Old World since then (not to mention the post-Columbian genetic history of the New World), Native Americans all descend from one to three populations of Paleolithic east Asians that migrated east across the Bering Strait. It is perhaps to no one's surprise that most trees of human genotypes typically find New World natives as a whole to form a group sister to East Asian groups.

Blond hair

The reason blonde hair is so common among Europeans and rare among most other places is that the mutation that produce blonde hair originally occurred somewhere in Europe (or possibly the parts of Asia near Europe) and has yet to spread widely. Red hair, in turn, is a mutation of the mutated gene that causes blond hair. Neanderthals had red hair, but it appears to be due to a different gene than the one that causes red hair in humans.

Blonde hair is not unique to Europeans. Solomon Islanders have it too, but it appears to be from a mutation in a different gene than Europeans.

Blue Eyes

As with blond hair, blue eyes are the result of a mutation in the human genome. The gene that causes blue eyes has been linked to a mutation that occurred in an individual that lived nearly 10,000 years ago on the north shore of the Black Sea, hence why the highest concentrations of people with blue eyes live close to that area (e.g., Scandinavia).

The thing is many of these genes may not confer any selective advantage, they may be neutral genes that arose due to genetic drift. For example Harding et al. concluded that the mutation which cause red hair confer no selective advantage in temperate climates, though they increase the risk of skin cancer in tropical latitudes. Similarly, the epicanthial fold may be linked to a gene that promotes hair growth but confers no selective advantage on its own. The same is probably true of other mutations, though I haven't dug through the literature to find precise examples.

This is the reason why pale skin and blonde hair are rare outside of the high latitudes. In temperate to polar latitudes they're harmless novelty genes and may even aid in vitamin D absorption, in subtropical to tropical latitudes they get rapidly removed from the gene pool due to being a one-way ticket to skin cancer.

Notably, part of the reason people from far western and far eastern Europe seem so different is because you aren't looking at the people in between. People in central Russia, central Asia, etc., show a mixture of traits. In fact, the Wikipedia page for red hair shows a young Uyghur girl from western China with both red hair and an epicanthial fold. Epicanthial folds are also increasingly common as you go west to east across Eurasia, they show up to with some frequency in eastern European populations like the Sami.

Height

Actually, normally people at the highest latitudes are shorter than those at lower latitudes (i.e., the Inuit), because shorter bodies help retain heat better.

Height is also highly variable and is often more subject to nutrition than genetics. If you look at a map of which countries are the tallest and shortest it maps more closely to GDP than it does gene flow. I'm reminded of a story of what happened when a large number of Guatemalan Mayans emigrated to the United States between the late 1970s and early 1990s. Guatemalan Mayans are some of the shortest people known, but this turned out to be due to poor nutrition growing up. Children of the original immigrants from Guatemala living on a more calorie-rich Western diet ended up being nearly 10 cm (almost four inches) taller than most Mayan children of that age.

Notably, the average height in Japan, China, and South Korea has skyrocketed over the last fifty years due to the increase in living standards.