Actually, I think that is a good practice, to summarize a proof before a detailed proof is given so the reader can look out for what is suspected, and rather skip or jump past some details that are uninteresting. So the summary is the cut to pieces of the proof and the proof is a filling in of the summary.
Now there are a lot of proofs that cannot be summarized by a few paragraphs, such as Wiles's FLT or Appel & Haken's 4 Color Mapping or even Veblen or Jordan on the Jordan Curve Theorem, and the reason no summary is possible is because they are fake proofs. A fake proof cannot be summarized because the hole or gap of the proof is made apparent in a summary. That a summary gets to the hole or gap of the proof, much quicker. And I have had experience with this quickness just a few days ago by the summary of the No Odd Perfect proof. My first summaries were having only one set of camps such as 15 is not perfect odd because of 1/3 camp with 2/3 camp needs a triangulation with another set of camps, the 1/15 camp with the 14/15 camp, so that the 5 and 10 in the first set and the 1 and 14 in the second set requires 15 to be divisible by 6 so that 1, 3, 5, 6 are the divisors that give those two sets of camps their total.
So, if a true proof of math is unable to make a quick summary, is because it is not a true proof.
The truth in science, no matter if math or physics, can be summarized, and if not able to made summary means the proof is fake. Somewhat like in literature, a story or fable has a theme that is summarized into a sentence. If it has no such sentence summary, means it is a incoherent gap ridden story.