...or perhaps doesn't.
But in relating the two accidents I'd suggest people are conflating two unrelated issues.
In the Sully case we're talking about a flare - converting airspeed into a brief burst of lift to reduce the vertical and horizontal speed on "touchdown". It may well be true that taking a further couple of degrees of AoA could have produced a different combination of horizontal/vertical velocity and attitude at touchdown. It is by no means certain that this combination would have been any better or worse than the combination that he actually used. Given that the combination used resulted in everyone getting off the aeroplane it's hard to make a case that a higher AoA would have been "better". It's quite possible that the higher AoA would have dragged the tail in the water and ruptured the fuselage, allowing it to flood MUCH quicker. But It digress - that's the Sully case.
In the OTHER case the aeroplane had entered the manoeuvre with excess speed and then slowed by retarding the power, so when the alpha-floor-limit manoeuvre was initiated the engines were running at a much lower power level, and so took more time to spool up than was available. The insufficient climb rate was due to a lack of THRUST, not a lack of LIFT. Further increases in AoA would almost certainly have had no effect on the rate of climb because the associated increase in drag would soak up the increasing thrust and just delay the achievement of PRoC. It might change the fuselage attitude, but it would be unlikely to change the flightpath.
The two situations are completely different.