Learn English – is ‘the same to ‘ better than ‘the same for ‘

There is an important difference of nuance, which the dictionary omits. The version with “all the better” suggests that the benefit is unexpected, or was not previously considered by the listener.

A well-known example of this phrase is in the fairy tale Little Red Riding Hood, when Little Red Riding Hood meets the wolf, who has dressed himself as her grandmother. Little Red Riding Hood is a little surprised at her “grandmother’s” appearance:

“Oh, grandmother! What big ears you have!” said Little Red Riding Hood.

“All the better to hear you with, my child,” said the wolf.

“But grandmother, what big eyes you have!” said Little Red Riding Hood.

“All the better to see you with, my child,” said the wolf.

“But grandmother, what large hands you have!” said Little Red Riding Hood.

“All the better to hug you with, my child,” said the wolf.

“Oh but grandmother, what big teeth you have!” said Little Red Riding Hood.

“All the better to eat you with!” said the wolf, who then jumped out of bed and ate up Little Red Riding Hood.

I think most native speakers today hear an echo of this scene from Little Red Riding Hood whenever they hear “all the better”. You could understand it as “Yes, but when you consider everything, that only makes the result better, not worse.”

Here’s a situation similar to your example but where “all the better” is natural:

“Oh no, the bus has broken down! The team will have to walk home. It’s five miles! We’ll be too tired to play on Sunday.”

“Your performance will be all the better for a little more exercise.”

You wouldn’t normally say “all the better” just to mean that getting some exercise will improve your performance. Here are some straightforward ways to say that, without the mixed overtones of “all the better”:

A little extra practice will improve their performance.

A little extra practice will make their performance better.

Their performance will be better because of a little extra practice.

A.1. To rephrase well using "who," you need to know a little more about the relationship between the President and the team. Possibilities might include: "Speaking as the President, who chose the team and leads the team" or "Speaking as the President, who chose the team and acts on the recommendations of the team," etc. More generally, if you want to use "who" and not "whom" you need to know what the President does with or gets from the team and not just what the team does for the President.

B.1. To me this sentence is ambiguous. It could mean that for most people e-mail has become a necessity, or it could mean that there is a subset of people for whom e-mail has become a necessity, and for most of that subset the solution is not available. For the former I would add a comma: "That is not a solution available to most people, for whom e-mail has become a necessity." For the latter I would say "That is not a solution available to most of those people for whom e-mail has become a necessity."

C.1. Yes, it means they are told how to vote. The phrase after the comma is reinforcing the point by saying that the people (the same people who are told how to vote) are forced to vote by people who have a hold over them. Arguably these are two slightly different points: they are forced to vote (versus staying home and not voting) and they are told how to vote. As you can tell from what I've just written, I think you can re-phrase to say "how to vote" instead of "for whom to vote." It is idiomatic in that it does not mean "told how to mark the box or pull the machine lever," but "told how to vote" is commonly used to mean "told which way/for whom to vote."