Rim brakes out of alignment and are unfixable I have a persisting issue where the caliper rim brakes which contact the metal part of the rim are too high and instead rub against the tyre on my front wheel. 
Previously, this issue persisted when I first got the bicycle. I got the brake caliper replaced but this did not fix it. I then replaced the wheel which solved the problem and the brakes were making appropriate contact to the metal rim. 

Unfortunately, I crashed the bike a few days later. I crashed the front wheel into a pole and I went over the hoods. The brakes had the same issue where they were too high and made contact with the tyres. I tried solving the problem by truing the wheel, despite not having a truing stand and doing it for the first time, I have the wheel which was not extremely out of true initially but improved it to as true as possible. However, the brakes are still misaligned. Unusually, the brake position is uniform across the entire rim and does not change position unlike what is expected in a crash where there will be a specific area where there will be an issue. 
(I have done all adjustments to the brake caliper as possible and moved them to the lowest possible position)

I have scoured the entire internet for a solution and similar problem yet have failed to find one. 

Is there a possible fix to this? I've tried to visualise what the causes are but the only thing I can think of is that the wheel was either hit on all sides and consequently uniformly shrunk in size which is obviously not the case.
That looks like the wrong-sized wheel:  a newer 622 mm wheel in an older fork designed for 27" (630 mm) wheels.

Per the great Sheldon Brown:

27 x anything except "27 five" and 609 mm Danish        630 mm      Older road bikes.