Looking for advice on MIDI wind controllers for DAW

I play saxophone and a bit of recorder and I like making music digitally in a DAW. However, I often struggle getting the more natural intonations and dynamics in the software. It seemed like this could be overcome by using an MIDI wind controller, but everywhere I look up about this, people only talk about using it as an actual instrument or practice instrument.

So my question to y'all:

Do these things actually work well as MIDI controllers for getting a more natural sound out of your VSTs?

And if so; which one would you recommend getting? Right now my eye is on the Roland AE-05, because of the pitchbend mouthpiece. (budget is around €400)