Why is request for a rematch button so obtrusive and flasyh?

I'm not hugely into rematches in the first place, but seeing it flash like a foglight, it basically force me into declining a rematch whenever I just want to review a game in peace.

Reviewing a game is supposed to be done in the "analysis".

You can review it in a new tab, that way you'll have left the game and there will be no rematch button.

Yes, these immediate rematch requests are typical for internet chess. In real non-blitz games it is absolutely common to analyze with opp after the game. And even Blitz games if they had interesting motives are analyzed or at least a few words are said about these. Real life chess is much more communicative.

The button seems aesthetically pleasant enough, and maybe even masks the fury with which your opponent has occasionally smashed his mouse for a rematch.

Declining shows the opponent that you don't wish to play another game right now, this helps them from wasting time instead of waiting for you to respond.

It could at least stop flashing when opponent leaves the game.

It usually happens that he'll offer rematch and leave few seconds after that, and you're left with neons blazing.

Usually when you decline they'll keep asking for a rematch. This has happened nearly thirty times in a row. If only they played the first match with such dogged persistence.

It is true, the constant flashing disturbs. Three times is enough. The Offer should also be removed if opp leaves.