Possible to remove time-based notifications on a Reminder item without it disappearing?

I am a casual user of the stock Reminders app. I see absolutely no need for time or location based reminders at all, because of the badge count on Reminders icon on my dock. However, all reminder items I've set up are automatically checked and come with a reminder notification, i.e.

When I enter "Complete Chapter 6 textbook summary" at 3am in the morning, the Reminder item shows up with the option 'remind me on a day' checked, with the time for reminder being 3am. So the task ends up being highlighted in red in my list as something I've missed out.

This makes no sense to me whatsoever. But moving on, I've also realised that manually unchecking the 'remind me on a day' option removes the item from my list altogether. It does not even show up under completed tasks. Everything about that reminder item just poofs out of existence!

Is there any way to fix this? I just need a simple to-do list with an option to turn off notifications when I like, and that shows me what I've already completed and what I need to get done. 3rd party app reccomendations are welcome, and thanks in advance for any tips!

Sidenote: I have an altogether separate Reminders list on my iPhone and everything seems to work fine. I don't sync Reminders between my Macbook and my iPhone, and I don't intend on doing it anytime soon.