From a frequentist perspective, there are some clear disadvantages of a sequential analyses. That is, if we are concerned with preserving type I errors, we need to recognize that we are doing multiple comparisons: if I do 3 analyses of the data, then I have three non-independent chances to make a type I error and need to adjust my inference as such. There's a variety of methods for accounting for this, but in short, for a fixed sample size and significance level, all of them end up reducing power compared to waiting until all the data comes in. So if you're looking at the power/subjects ratio, you can't beat a fixed analysis, although as you point out, often that's not necessarily the most important metric.
Theoretically, from a Bayesian perspective, there's nothing wrong with using a sequential analysis. Since Bayesian decision theory generally does not worry about type I errors, there's nothing wrong with multiple peeks. However, in practice, it's a lot more of a gray area. Derived prior distributions don't really capture our knowledge before seeing the data, but we can hand wave this issue away by saying that the likelihood will typically dominate the prior, so this isn't an issue. But if we do a sequential analysis, we may be analyzing the data when we have very little data. Suddenly, miss-specification of the prior becomes a really big issue!
To be clear, I think sequential analyses are a very good idea. But there are downsides.