Henry Tudor had english parents, he could claim the throne much easier than Max, a complete FOREIGN RULER from AUSTRIA. WHY would Max want to claim england rather than support Richard, who is his ALLY against France???
Like hell France is gonna permit Max and Marie to grab england too. Anne of France is gonna prevent Max from taking england, if for nothing else to prevent him from becoming a even bigger threath. Spain and Portugal is fighting the moors, they can't help Max.
Not to mention, wasn't Friedrich III in contention with Matyas Corvinus at the time?