That's dangerous. Esp. in my big games where I end up with ~40 systems at the end.

I rather get a message that a system has nothing to do. In using P3DP/Planet Cracker I tend to forget adjusting building queues of system where these are running. And then it turns out that I could've built an important improvement 10 turns ago. 

It's tempting to use these infinite turn actions. However, a feature regarding them should be fleshed out a bit more. Otherwise it'd probably do more harm than good in my games.

Oh, you are absolutely right that a system should FIRST be mentioned in the construction-finished pop-up and also in the the end-turn reminder (empty queues).

However, once you ignore that reminder, and still press turn, without anything being in that construction queue at this point, ONLY THEN the system should, for this one turn only, inject the conversion option. 

The following turn the reminder would pop up again for the same systems. 

As for "infinite construction options", I agree that they should show every turn as part of the pop-up. After all, they "finished" something. They just keep repeating finishing it.

A solutions that would be a little bit more refined, would be to only include them in the pop-up, when a research has been finished, as this often times means that you have new options available to build.

https://www.games2gether.com/endless-space-2/ideas/1488-construction-complete-notification-when-infinite-construction-system-has-new-building-option