You can always get the designer mode password; it lets you see what NPRs are doing and also delete stuff if you're stuck with a neverending battle (or just impatient).
Or do what I do and don't start with any NPRs
You can, but entering SM/designer mode reveals a lot of things as a side-effect. And destroying the exploration aspect of the game would kill a significant portion of the fun for many of us.
And removing NPRs (potentially real opponents) altogether isn't an option for me either, as fighting nothing but Precursors and Star Swarm would get old fast. The whole universe would feel empty and lifeless. Imagine playing any Civilization game with nothing to look forward to but wiping out barbarians.
If you don't want to, you don't have to look at much with the designer mode; you can just use it to end any everlasting fights. And I didn't say play without NPRs, I said start without NPRs. The game will add them in as you expand, but it's having them around from the beginning that really causes the 5 second turns.
I'm guessing 5-second increment periods can also happen if the NPR gets into fisticuffs with Precursors and Star Swarm.
But now, honest question: how could you stop the offending battles
without seeing much? You'd have to look upon the true extent of the universe/galaxy, probably inevitably seeing where the NPR, Precursor and Star Swarm systems are,
and find the likely previously unknown system and the culprit vessels before you can wipe a side out and get rid of the engagement.