Yet it still failed.

We're not talking about a new wheel though. It's not a question of is it possible to weld. It's a question of is this particular wheel safe...? By nature if a wheel has a bend in it, say its hit a brick, enough to crack the metal there's two other points where the rim had to bend in either side to allow it to happen, for example. Ok, bend it straight fill with weld. Make it round. But it's a bodged weld in this case presumably, with a good chance of two more elsewhere it seems to me.
I'd want to see that wheel stripped completely to the metal. One bodged repair, to two. 3 maybe? Filler under the paint? It might be fine and the pic shows the full extent of it, but who honestly knows what's gone on with that wheel....? Nobody, that's who.
Opinion asked for, opinion given.

although possibly not fully explained at the start, who'd of thought it would get this much attention? But there we are.
