That's what AoA is though. It's the relative wind angle over the wing. The wind matters. You can't calculate AoA simply from pitch or vertical speed or something like that.

IIRC Boeing calculates a synthetic AoA value from the inertial reference unit in the 777 and 787, so you can derive it.

Is there another method to measure wind direction, that doesn't involve a small physical winglet?

Another way would be to stick a tab in the slipstream, and measure the pressure on its leading edge and both sides. Or just put a strain gauge on the mount of the tab and measure the bending forces (and this would have no ports to freeze or moving parts to jam). I bet there are lots of ways.

P.S. I bet you could even put a strain gauge on the wing spar to measure the bending force on the wing, couple that with other inputs like airspeed, and come up with a reasonable AoA value.

The problem with such approaches is that you have to model all the environmental and performance factors that could cause an identical pseudo-AoA to be calculated, in all flight modes. And to do that you need a range of sensors, all redundant... so now you need additional input validation and sanitisation.

For example, measuring slipstream over the wing is not sufficient. You need to known the pressure ratio between above and below, so there's two sensors. But airflow over a wing is not contiguous or straight, so you need more spanwise sensors to start averaging. And the inboard wing will stall first and give erroneous data, so you need to detect that and disregard it...

Rather than just measuring the raw value at source.

No need to measure pressure at the top and the bottom if you use a strain gauge on a wing spar to measure the net force bending the wing.

I'm sure a function can be constructed that takes that input, along with the airspeed, and produces AoA. It can be used as a crosscheck with the AoA sensors. Since it takes airspeed as another parameter, it can also crosscheck the pitot tubes.

It can be derived using static ports that measure air pressure at several locations.