Set is specially overloaded for Part in order to allow in-place modification of the expressions:

a = x -> 2;
a[[1]] = 1; a

1 -> 2

It is documented on the Documentation page for Part (the first point under "Details" section):

You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. »

Your function hoge doesn't Hold its arguments and hence passes to Set the extracted variable instead of the Part expression, what explains why it "works" for you:

hoge[x_, y_] := Hold[x = y]
a = x -> 2;
hoge[a[[1]], a[[2]]]

Hold[x = 2]

For your particular purpose the simplest approach is to replace Rule by Set:

Clear[x, y, z]
{x -> 2, y -> 5, z -> x + y} /. Rule -> Set

{2, 5, 7}

Another method is to Apply Set effectively replacing the head Rule by Set:

Clear[x, y, z]
Set @@@ {x -> 2, y -> 5, z -> x + y}

{2, 5, 7}

Inside of Do:

Clear[x, y, z]
Do[Set @@ a, {a, {x -> 2, y -> 5, z -> x + y}}];
{x, y, z}

{2, 5, 7}

Set is specially overloaded for Part in order to allow in-place modification of the expressions:

a = x -> 2;
a[[1]] = 1; a

1 -> 2

It is documented on the Documentation page for Part (the first point under "Details" section):

You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. »

Your function hoge doesn't Hold its arguments and hence passes to Set the extracted variable (a Symbol) instead of the Part expression what explains why it "works" for you:

hoge[x_, y_] := Hold[x = y]
a = x -> 2;
hoge[a[[1]], a[[2]]]

Hold[x = 2]

For your particular purpose the simplest approach is to replace Rule by Set:

Clear[x, y, z]
{x -> 2, y -> 5, z -> x + y} /. Rule -> Set

{2, 5, 7}

Another method is to Apply Set effectively replacing the head Rule by Set:

Clear[x, y, z]
Set @@@ {x -> 2, y -> 5, z -> x + y}

{2, 5, 7}

Inside of Do:

Clear[x, y, z]
Do[Set @@ a, {a, {x -> 2, y -> 5, z -> x + y}}];
{x, y, z}

{2, 5, 7}

Set is specially overloaded for Part in order to allow in-place modification of the expressions:

a = x -> 2;
a[[1]] = 1; a

1 -> 2

It is documented on the Documentation page for Part (the first point under "Details" section):

You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. »

For your particular purpose the simplest approach is to replace Rule by Set:

Clear[x, y, z]
{x -> 2, y -> 5, z -> x + y} /. Rule -> Set

{2, 5, 7}

Another method is to Apply Set effectively replacing the head Rule by Set:

Clear[x, y, z]
Set @@@ {x -> 2, y -> 5, z -> x + y}

{2, 5, 7}

Inside of Do:

Clear[x, y, z]
Do[Set @@ a, {a, {x -> 2, y -> 5, z -> x + y}}];
{x, y, z}

{2, 5, 7}

Set is specially overloaded for Part in order to allow in-place modification of the expressions:

a = x -> 2;
a[[1]] = 1; a

1 -> 2

It is documented on the Documentation page for Part (the first point under "Details" section):

You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. »

Your function hoge doesn't Hold its arguments and hence passes to Set the extracted variable instead of the Part expression, what explains why it "works" for you:

hoge[x_, y_] := Hold[x = y]
a = x -> 2;
hoge[a[[1]], a[[2]]]

Hold[x = 2]

For your particular purpose the simplest approach is to replace Rule by Set:

Clear[x, y, z]
{x -> 2, y -> 5, z -> x + y} /. Rule -> Set

{2, 5, 7}

Another method is to Apply Set effectively replacing the head Rule by Set:

Clear[x, y, z]
Set @@@ {x -> 2, y -> 5, z -> x + y}

{2, 5, 7}

Inside of Do:

Clear[x, y, z]
Do[Set @@ a, {a, {x -> 2, y -> 5, z -> x + y}}];
{x, y, z}

{2, 5, 7}