I think that mostly depends on where you live.
Who cares about reputation? Some random girl rejects your approach who cares? Probably never see you again and she doesn't even know you.
Men who live in metro areas with millions of people are not going to have problems with reputation. The areas are too populated for that to happen.
In most daygame or nightgame settings, after a failed approach, I never saw the woman again. It's difficult to see the same person again when daygaming in retail settings (malls, bookstores, grocery stores, etc).
If a man decides to do approaches within his own gym, then he will likely see the same woman again after an approach, a failed first date, or after a relationship fails. I've dealt with that and it is unpleasant. I had a harsh rejection at my gym once from one of the most attractive women who attended that gym. I had to see her for a while until she changed gyms.
It seems almost everyone does "night game' to an extent hitting on girls at bars.
This sentence would have been more true 15-20 years ago than it is today.
Night game has been affected by online game. In the 2000s, when dating websites were around, the impact on night game was minimal. However, once dating apps replaced the dating websites in the early 2010s, the apps became more of a thing than the websites were in the 2000s/early 2010s. Also, over time, sending DMs on social media started to become more a thing. I arranged dates in the mid-2000s sending DMs on MySpace. That was somewhat unusual then. Now, far more men are arranging dates in the DMs on Instagram and on Twitter to a lesser extent.
It's been possible for at least 10 years to arrange plenty of dates solely using swipe apps or DMs on social media without ever doing approaches at bars. I'm not including daygame as part of this analysis because daygame has always been a bit of a niche. However, daygame has always had the potential to replace night game for arranging dates. However daygamers typically will need to go to bars to have a few dates before having sex with a woman.
Night game is the default form of in-person game for men who don't use the tech methods and don't have a social circle capable of arranging dates. The tech methods have made night game a bit redundant. Additionally, social circle has been in a long term downward trend for decades. Fewer people have had viable social circles for decades.
But "day game" going to malls or large outdoor areas or etc seem to be a lot more rare and unusual for people. What do people think?
Daygame is rare. If you look at the chart from above closely, there's nothing about daygame there. I would guess daygame would be lumped in with bar/restaurant meetings, because I think the researchers had used the classification of "bar/restaurant/other public place" in 2009. Other public place would count as daygame.
Daygame isn't that common because most men don't have the ability to randomly approach women in retail settings (malls/grocery stores/bookstores etc) or outdoor areas (parks, walking paths, etc). Most men need to do dedicated approach sessions taking hours outdoors and that's not fun to do. I can't tell you how unpleasant it feels to do a 2 hour approach session outdoors and not come away with any dates or any approaches that lasted longer than 60 seconds. It feels like a giant waste of time. Additionally, indoor retail approachers will also need to linger around that setting for hours to find a woman receptive to the approach.
Doing that shiit sober is too tough for most men, especially men with lower testosterone levels than the men of 30-40 years ago. The men of 30-40 years ago didn't even like doing that.
There are still enough men out there willing to do daygame because they don't enjoy alcohol/loud music/late nights, aren't having good experiences on swipe apps (most men don't), and don't have social circle options.