But if you're talking about a private cubicle within the main changing room, then the doctor would first have to check that there wasn't anyone already in the main changing room getting changed first/hang about waiting until it was completely empty(not ideal if they're rushing to start a shift) in order to walk through it to get to the cubicle.
Then even if it the main changing room was empty at that point, what happens if someone comes in while the dr is changing in the cubicle? The dr would come out and you'd still have the exact same issue as one of the occasions described by the nurse-she was part way through getting changed, the dr came in and the nurse felt uncomfortable and left.
Same if it was the other way round - nurse comes in first and goes into cubicle, doctor comes in afterwards, starts getting changed in the main area, nurse comes out of cubicle and sees the dr undressed.
Not to mention the fact that even though this nurse is the one named there might very well be other staff uncomfortable with the whole situation, from either perspective.
besides which the vast, vast majority of sexual assaults, peeping tom incidents, people recording others (either live or putting cameras in changing rooms or toilets) happen in mixed sex changing rooms with cubicles.
The best scenario/least potential for issues would be to only have multiple, completely self enclosed rooms (like disabled toilets usually are), but you'd have to have enough for everyone to get changed at the same time (very expensive given the shift nature of the NHS and takes up lots of space which is then unused for most of the day).
If you only had a few cubicles and no guidance saying who has to use them and who can/can't use the communal changing rooms, then you'd still be in the exact same position as now - with no recourse if the doctor (or any other trans member of staff) chooses not to use them (whether because making a stand/all the cubicles were already occupied and didn't want to wait or any other reason).