Bonjour Chris et Maarten !

Here, the "difficulty" comes from the fact that you can translate "arriver" by "to get there" in English, i.e. the "there" is included in the meaning of "arriver".

As Maarten mentioned, unlike "aller", "arriver" is therefore usually used on its own.

But here's an extra layer: though "j'ai failli y arriver en retard" is grammatically correct, it creates an extra ambiguity in French, when you consider the expression "arriver à [faire]" = "to manage to [do]".
"Y arriver" is used (almost, though I can't really think of an example) exclusively in that context (j'y suis arrivé = I made it, I managed), which makes the previous sentence very awkward to native ears :) 

The most colloquial therefore remains to use "arriver" on its own.

I hope that's helpful.

Bonne journée à tous les deux !