I haven’t heard of any specific uses for the time of Meridian Passage of Aries, but I can think of a potential use for it. You can use it to identify stars or planets that are crossing the meridian at twilight, simply by subtracting the time of sunrise (or sunset) from the meridian passage of Aries. The result will give you the SHA of anything crossing the meridian at twilight; all you have to do is look in the Almanac for objects with a similar SHA, and they should be approximately on the meridian at that time. This could be useful if you wanted to find a star that was crossing the meridian at twilight, so that you could use it to quickly determine your latitude (if Polaris wasn’t visible or you were in the southern hemisphere). For example, if I wanted to find a star near the meridian today (4/4/22) at latitude 40N at sunset, I just look up the time of meridian passage of Aries (1105) and subtract the time of sunset (1828), add 24 (since it’s negative) and I get 1637. If I multiply this by 15, I get an SHA of 249. Browsing the list of stars in the Almanac, I can see that Procyon is pretty close to this (SHA of 245). So at sunset at 40N, I can predict that Procyon is very near the meridian and can provide a nice E-W LOP to include in my round of sights.
I’m sure there are other uses for it, but that’s the first one that came to mind. It also conveniently fills the space at the bottom of the Aries column, so maybe that is its primary purpose!