There are a few drawbacks to focusing on continuity in a series like the Zelda series, which can have an impact on a game designer's freedom. First of all, if the game designers wanted a Zelda game to fit into a continuity at some place, that choice would necessitate certain world-building choices. For example, if Nintendo made the decision to make a Zelda game take place immediately after A Link to the Past, they could not use Gorons or Kokiri, or make any non-human a sage, without having to make a lot of explanations inside the game. In order to uphold continuity, a game designer cannot make glaring contradictions to previous games in the series. Thus, the game designers are bound by the decisions made by previous directors and writers.
Furthermore, putting games in the same continuity mandates the presence of continuity nods, like what appear in Twilight Princess and Wind Waker around the stories of ancient heroes wearing green. However, relying too much on continuity nods to explain story details can cause problems if your audience hasn't played the previous games. For example, the fact that there are Triforce marks on the hands of Link, Zelda, and Ganondorf in Twilight Princess that represent the power of the Triforce pieces is something that only makes sense to someone who has played Ocarina of Time or Wind Waker, particularly since the word Triforce is not mentioned once in Twilight Princess. However, there are plenty of gamers who have played neither of those games. You can't count on your audience's knowledge of the series. Relying on continuity to fill in storytelling gaps can be problem. Ideally, every videogame should be self-contained enough to make sense by itself.
However, there are other story telling methods and ways of managing continuity that have very successful precedent in film and television. One example is the Mobile Suit Gundam series. Originally, all Gundam series were part of a single continuity. However, after the movie Char's Counterattack, the time jumps in the story were big enough that the entire setting had changed too much to even be recognizable. However, while the series had lost most of the advantages of continuity, it was stuck with trying to maintain some degree of consistency. This eventually resulted in Mobile Suit Victory Gundam, which was very poorly received. Afterwards, the creators of Gundam created what came to be known as Alternate Universe series. In these television series, the creators could still benefit from the name recognition built by the original continuity, but had much greater freedom to experiment. For example, the original universe had physics built around the existence of the Minovisky particle, which explained all of the fancy beam weapons and flight technology. However, later alternate universe series were free t completely ditch the Minovisky particle and its wonky effects if they wanted to. This resulted in series like Gundam Seed, which was partially an alternate retelling of the original series with the addition of genetically engineered super-humans. The creators simply had more design space.
A similar, yet somewhat different, example can be found in the Godzilla movies. There are actually at least three separate continuities of Japanese Godzilla movies. They all share one thing in common: they all assume that the original Godzilla movie took place. Other than that, they are all completely independent of each other. There isn't even a in-story explanation for this divergence either. I guess I will call this a Branching Alternate Universe approach.
Another example can be found in the James Bond series of movies. In the James Bond movies, there are certain characters that are constantly recurring: Bond himself, Moneypenny, M, Q, and sometimes villains such as Blofeld. However, it is hard to say that the movies are really in a single continuity. If they were, James Bond would be over 60 years old by the time of Die Another Day. However, he clearly isn't. And while there are some continuity nods, they are not very common. In a way, this is the closest model to The Legend of Zelda series. While the Bond movies try to generally maintain consistency of the personalities and quirks of the characters, they don't maintain consistency in the world at large. This allows the designers to rely on the familiarity of the characters while maintaining almost complete freedom in storytelling.
Keeping these kinds of continuity in mind can be a helpful thing, particularly when most videogames are designed without much forethought for sequels or overarching metaplots. So, when game developers sit down to plan out a sequel to a popular franchise, they should ask themselves what kind of continuity would best help them.