Would it be possible to add a checkbox in the "finish playthrough" window, that would exclude the completion time from the global statistics, similar to the "Do you know how long you played?" one, but that would still show the time on the "My Completion" page?

My reasoning behind this is, so completion times of freeplay sessions dont distort the campaign completion times, but you could still track the times for yourself. This would be useful for games that focus on freeplay, but still have a campaign (for example Transport Fever 2 or Civilization). Freeplay is the Meat of these games, but completion times of freeplay will differ starkly from session to session and are completely unrelated to how long the campaign would have took.
Alternatively perhaps a way to set if the time was for a campaign playthrough or a freeplay session.

I think that a freeplay option added to the completion types sounds like the way to go for something like this, rather than a toggle checkbox for all playthrough types. Of course, that's assuming there isn't some implementational hurdle involved.

I'm thinking that by selecting freeplay (or whatever naming scheme is decided upon) for your playthrough option, that it wouldn't be added to any global statistics by design, while the rest of the options would be business as usual.

I think adding a generic "include with community statistics" option (turned ON by default) would be the way to go. My only concern is that the Add Completion modal already has a variety of options / questions and this would be another one that would almost always be left in its default state.

That being said, the system does have a mechanism in place to exclude certain completion times (which is how the ones without a time are ignored), so we can manually kick some of yours out if you want

Haha, welp, overruled I guess. The main reason I thought adding a new playthrough type could have been the better choice earlier was because it covers an uncommon style of playthrough that isn't explicitly represented by the existing options.

In retrospect, a freeplay playthrough could be entered as one of the "Core Game + whatever" options if need be. Round peg in a square hole, but it works, lol.

Actually, I think I misread your post (not sure how since it's pretty clear to me now, maybe I needed sleep) Having a completion type that's excluded from the aggregated statistics would also be easy to do (and I think I already exclude Speed Run). Plus it wouldn't require a new setting / checkbox. The only downside really is that we show the various completion types throughout the site, so I'd need to modify a variety of pages to use the new one or it could just be ignored altogether (which might make sense since it's likely not going to be used heavily and the times will vary wildly). So maybe just slap a section on the Game Details page, modify the aggregation logic to ignore it, and call it a day?

Seems good enough to me.