It wasn't easier to track via the moon, it was MUCH easier. How exactly do you calculate the solar cycle in ancient times? You won't have accurate-enough timekeeping for centuries to know the exact day of the solstice by tracking duration of day, you're basically stuck trying to accurately measure shadows or the angle of the sun, which takes years of observations to establish. That's a lot of effort for anyone and is very not-portable. It's something only the elites can do or will care about.

But anybody can see the moon, and it's not even 10 fingers' worth of counting from full or new to a quarter moon. It's very easy for everyone to observe and to track with. It's also not ambiguous--a full moon is a full moon, you might be off by a day at most, and there would be general agreement in a community.

And the primary thing you need timekeeping for is agriculture (because that's what 90% plus of the population do, and what 100% eat). But, due to weather variability, knowing when spring astronomically begins doesn't help you all that much. Temperature trends, rain, likelihood of a frost, all of those are more important. IIRC, lunar calendars (the Islamic calendar being a notable exception) usually start counting in the spring, when X crop needs to be harvested and Y crop planted for just this reason.