I have noticed on some of the later AIWA models that tape azimuth is not adjustable. This can be extremely annoying especially when playing material that was previously recorded on Dolby C, which is very sensitive to misaligned heads. I have mitigated this issue by making a 1 & 10kHz test tape on one of my fixed azimuth recorders and re-calibrating my main cassette recorder to match that.

Another annoying feature is the lack of symmetry in the fixed azimuth auto reverse units when playing the reverse side. I have noticed that side A might be perfectly in alignment but auto reverse onto side B and things sound dull and off centre. Flipping the tape seems to temporarily resolve this although this is not ideal. In other words, what was the point of having the auto reverse? Earlier models such as the HS-JX303 or HX-JX505 do not seem to suffer from this issue, but later ones such as HS-PX1000 and HS-JX707 do. Although neither earlier models mentioned have Dolby C as an option, they do allow independent azimuth adjustment on both sides of the cassette.

Does anyone else find it annoying, or do you avoid playing cassettes in these slightly problematic units in the first place?

I think I have a AIWA with no algnment on it.
But it might have an odd method to align it.
Do you have a manual for it?
Never seen a cassette player without an alignment screw.

I have the service manual from AIWA for the HS-JX707 and under azimuth adjustment it states clearly that there is no adjustment for this model.