Learn Russian: Я никогда не видел подобной красоты.

Because in this sentence, we aren't using the preposition подобно (like/similar to). We are using the adjective подобный (such/of such a kind). It acts as a normal adjective modifying the noun красота (beauty), so they must agree in gender, number, and case.

Why are подобной красоты in the Genitive case instead of the Accusative case?

This is an example of the Genitive of Negation. When a transitive verb like видеть (to see) is negated (не видел), its direct object often takes the Genitive case rather than the Accusative. This is especially true for abstract nouns like красота, emphasizing a complete lack of the thing mentioned.

Could I use такой instead of подобной in this sentence?

Yes! Я никогда не видел такой красоты is very natural and actually more common in everyday speech. Using подобной adds a slightly more elevated or emphatic tone, translating closer to "beauty of this kind" or "comparable beauty."

Why does this sentence use the imperfective verb видел instead of the perfective увидел?

When talking about an experience you have never had in your entire life up to this point, Russian almost always uses the imperfective aspect. This places the focus on the general fact of the action (or lack of it), rather than on a specific, completed result.