During my childhood, here, usually only preschool children had their temperature taken rectaly.
In my case, after I reached 7 years old my mom started to use alternately - rectal and axial till I was 12.
Usually, if wasn't any hurry, I was let to introduce the thermometer myself under my arm ( axial way ) and after around 5 minutes my mom had ask me to give her for reading, but sometimes (at least 50 % from cases), she had doubts that the temperature displayed was accurate, so, she insisted to take again my temperature in the "baby way". Mostly she suspected me that I moved my arm and the thermometer wasn't keept propely anymore (I was a skinny hiperactive kid, and I must to admit that her reason was true), and second, because once, when I was 9, I had try to fake my temperature for a school skipping...
If my mom was hurry, she always proceed for a rectal check from the first time...
My grandmother always used the "baby way" till I was 12 almost 13. She was a former military nurse in WW2 and later a orphanage nurse, so, no no sense!
For me, since I was in the kindergraten, I always felt myself shy and embarrased because of my exposure, but somehow at least it was fair for me because most of the kids around my age from my circle was treated in the same way.
When I was a bit older and most of my cousins around my age was check ONLY under arm like most of the other kids - I started to feel myself treated unfair, like I was still a baby or a todler...