This tendency for weather (and other) events to even out over time is sometimes called the Law of Averages. June has worked out nicely in this regards, but of course that's not always the case. Large-scale circulation features can sometimes lock you into a pattern that is unusually cold or warm. Ditto for precipitation. For the Law of Averages to work, one typically needs a fairly long sample size.
However, we have a problem when it comes to weather: climate change. The statistics of weather are changing. The National Climatic Data Center now updates their "climate normals" every 10 years so that they better reflect more recent climatic conditions. For instance, the "normals" you see on the news each night are currently averages for 1981–2010. If you go back a few years, they would have been for 1971–2000. Sometime after 2020, they will be updated using data for 1991–2020. So, when you hear a day was near normal on the news, that really means near average for 1981–2010.
So, over short time periods, the Law of Averages often doesn't work well due to the small sample size. Over long time periods, it will also prove problematic as the climate warms during the 20th century.
In some parts of the world, it can also be a problem at intermediate time periods of say a decade. For example, the law of averages hasn't helped much with the Southwest drought over about the past decade. Sometimes things simply don't average out, at least in a timely fashion as one might hope.