We have just passed one of the solstices and are approaching aphelion. The two events are close but not simultaneous. There is no very obvious (to me) reason why the two should coincide or be close. Is there a less obvious reason why they are close? If so, is the gap closing, growing, or remaining approximately constant?
The two coincided about 800 years ago. The December solstice and perihelion date coincided in 1246, 773 years ago.
There are many different concepts of what qualifies as a "year". Three of them are the sidereal, tropical, and anomalistic years. The sidereal year measures how long it takes for the Earth to complete one orbit about the Sun with respect to the remote stars.
The tropical year measures how long it takes for the Earth to pass from one March equinox to the next. The tropical year is about 20 minutes shorter than the sidereal year due to the slow changes in the Earth's rotation axis caused by the Moon and the Sun.
The anomalistic year measures how long it takes for the Earth to pass from one perihelion to the next (or one aphelion to the next). The anomalistic year is about 7.8 minutes longer than the sidereal year due to gravitational perturbations from the other planets, with Jupiter and Venus dominating over all the others. The tropical year is thus shorter than the anomalistic year by about 28 minutes. That the tropical year and anomalistic year have slightly different frequencies means that there is a very slow beat frequency with a beat period of about 26000 years.
Human civilization arose about half of this period ago (about 12000 years ago) when the last glaciation ("ice age") ended. At that time, the anomalistic and tropical years were almost 180 degrees out of phase with respect to where they are now. The end of a glaciation typically occurs when northern hemisphere summers coincide with perihelion. That makes summers in far northern latitudes short in duration but rather hot.
One of the key proxies regarding whether glaciations start or end is the mean July temperature at far northern latitudes. When perihelion occurs a few weeks after the June solstice, the short but hot summers that result makes snow from the previous winter melt rather than build up. The melting that results from such short but hot summers triggers a positive feedback that makes the end of a glaciation very rapid, in a geological context of "rapid".
To clarify things,
So, there is no particular reason in orbital mechanics; it just happens that we live in an era when they are close together?
Or maybe not. The end of the last glaciation, which occurred about 12000 years ago, massively spurred human development. The cycle then was almost exactly opposite what it is now. It took about 10000 years for humanity to develop to a somewhat advanced level (e.g., Roman Empire level), and then only another couple of thousand to develop to the stage where we are now. Whether humanity can survive for another 13000 years without wiping itself out will determine whether this was happenstance.