How to convert a Dataset into an indexed dataset / association-of-associations given a column header?

data = {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, <|
    "letter" -> "b", "foo" -> 3, "bar" -> 4|>, <|"letter" -> "c", 
    "foo" -> 5, "bar" -> 6|>};
dataDS = Dataset[data];

ClearAll[f];
f[ds_Dataset, ch_] := ds[Apply[Association], #[ch] -> KeyDrop[#, ch] &];

f[dataDS, "letter"]

(Using the definition suggested by @WReach in the comments.)

First answer

data = {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, <|
    "letter" -> "b", "foo" -> 3, "bar" -> 4|>, <|"letter" -> "c", 
    "foo" -> 5, "bar" -> 6|>};
dataDS = Dataset[data];

ClearAll[f];
f[ds_Dataset, ch_] := Dataset@Association@Normal@ds[All, #[ch] -> KeyDrop[#, ch] &];

f[dataDS, "letter"]

ClearAll[f0]
f0 = GroupBy[##, Association @* KeyDrop[#2]] &;

Examples:

ds = Dataset @ {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, 
        <|"letter" -> "b", "foo" -> 3, "bar" -> 4|>, 
        <|"letter" -> "c", "foo" -> 5, "bar" -> 6|>};

Row[{ds, f0[ds, "letter"], f0[ds, "foo"], f0[ds, "bar"]}, Spacer[10]]

You can also do:

ClearAll[f1]
f1 = #[GroupBy[#2] /* Map[Association @* KeyDrop[#2]]] &;

Row[{ds, f1[ds, "letter"], f1[ds, "foo"], f1[ds, "bar"]}, Spacer[10]]

and

ClearAll[f2]
f2 = #[GroupBy @ #2, All, First @ Normal @ Keys @ KeyDrop @ ##] &;

Row[{ds, f2[ds, "letter"], f2[ds, "foo"], f2[ds, "bar"]}, Spacer[10]]

Related to kglr's answer, here's a slight variation:

ds = Dataset @ {
    <|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, 
    <|"letter" -> "b",  "foo" -> 3, "bar" -> 4|>,
    <|"letter" -> "c", "foo" -> 5, "bar" -> 6|>
};
groupByKey[ds_, key_String] := GroupBy[ds, Function[Slot[key]] -> KeyDrop[key], First];
groupByKey[ds, "letter"]

Of course, you have to be confident that the key values you're grouping by is actually unique, otherwise you'll be dropping rows.