EVOO on EVERYTHING.
But I'm Italian, so, take that for what its worth.
I'm Italian, and I keep multiple olive oils in my pantry. EVOO is not the right OO for every application.
As for making a rub or seasoning stick to a piece of meat or some veggies, I use a light OO, or a canola. On veggies, I use a spray oil -- usually canola.
I have about ten oils in my pantry. Every one has its one purpose.
Going back to the OP. I generally don't use any oil, or mustard, or anything else to make my rub stick. When I have experimented with oils and dressings, I haven't found a major difference in the final product. But, it certainly didn't hurt anything.
On a short cook, like a steak done in ten minutes, spices and oils make a lot more of a difference than they do on a long, slow cook, IMO.
Low and slow, again IMO, is more forgiving than a quick grill.
CD