To me, the car just looks too high. I'd want to lower it about 2".
But I agree on filling the wheelwell, and not seeing a gap above the tire.
But yes, a 70-series will tend to fill the opening a bit better; but it's likely to be a taller tire.

FWIW: I'm not a fan of what we in the US call a tire-cross; hope you have a proper socket, extension & etc for the lug nuts.