As much as I'd rather Des as AW coach, I'm not sure its fair to blame lack of a European tour on Hay. Likely completely outside his control and I'd be surprised if NZF could pull the money for it out of their asses considering the financial impacts of the last 14 months.
https://www.stuff.co.nz/sport/football/nz-teams/125160480/nz-football-records-large-surplus-in-2020-but-already-has-plans-for-spending-it
Would have thought that Spanish facility that AWs were based at for their behind closed doors friendly against Canada in 2018, was fairly cheap.
Or Hay could have reached out to his old mate Declan, to see if the Torslanda training facility in Sweden could have hosted 20-30 odd footballers & coaches for a week!! What about another one of his contacts Roberto Martínez - any room at a Belgian FA training facility.
I have no strong view on whether Hay is a better coach than Buckingham or vice versa. I just don't think Des would have stayed around in NZ right up to Tokyo. He would have packed up his suitcase & laptop, and flown off to maximise any actual hands on training opportunities in Europe - knowing that any window to be with his players over next 12 months is damn important. And then from there found his way to Nippon.