Repetition/Looping: I am extremely confused

I recently read that advanced writers keep the same or closely related subjects at the beginning of sentences or clauses.

This:

The President ..............................................proposed lower taxes.
He  ..............................................................drafted the proposal in December
and......................................................... hoped it would be passed within the next year.
The president.............................................. estimated accurately, and as such,
He ...............................................................will likely be re-elected. 

Is supposedly better structured than:

The President's proposal..........................promised to lower taxes.
A draft......................................................was written in December.
The president............................................hoped it would be passe within the next year.
This president's estimation........................................was accurate.
The people...............................................will most likely re-elect him.

By keeping the beginning of each clause or sentence as related as possible to the original (and ultimately, most important) subject, the writing is easier to follow. The subject is the president in the first, but the subject is the president, his proposal, a draft, his estimation, and the people, in the second. Though I understand this in concept, and in how it'd work to keep the paragraph easier to follow, I also feel like it's beating the reader over the head, and does not allow for subtle transitions.