What's the meaning of using Bootstrap? Why should resampling from sample set have any difference? I just learned Bootstrap Method from my Statistics course. The teacher says that the whole population is unknown, however we have some sample set $\mathcal{D}$ with sample size $N$. Then we use this sample set $\mathcal{D}$ as population and sample from $\mathcal{D}$ with replacement to compute all statistics we want (like mean, variance, median, or train a ML model from resampled set, etc.). We will have a fantatic result from this method (average result from all resampled sets).
However, I totally cannot understand the spirit of resampling from $\mathcal{D}$. For example, the actual distribution is Bernoulli distribution with $p = 0.5$. I get a sample set $\mathcal{D}$ with sample size $100$ from this distribution with $52$ of one and $48$ of zero. If I resample with replacement from $\mathcal{D}$, it just means that I have a Bernoulli distribution with $p = 0.52$.
My Questions:

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*Why shouldn't I directly compute all statistics I want from $\mathcal{D}$? No matter how many times of resampling, I can only get converged $\text{mean} = 0.52$ and $\text{var} = 0.52 * 0.48$. I don't think I can get any improvement from resampling or I can even recover the underlying distribution. Am I right?


*What's the loophole of my arguments? What's the advantage of Bootstrap? For example, is there anything I cannot get from sample set $\mathcal{D}$ but from $Bootstrap$?

The main application of the bootstrap is to learn something about the sampling distribution of the statistic, not the statistic itself. While it is easy to calculate an estimate $\hat D$ of the ratio $D$ of two medians from data, there might not be a reliable formula for its standard error $\sqrt{\text{Var}(\hat D)}$. You would need that to construct simple confidence intervals. The bootstrap provides you with methods to estimate measures like $\sqrt{\text{Var}(\hat D)}$.
