On a hill in high, with the mower going and thick grass - yep totally normal. Should be shipping to low for that. It will give you a ton more power and keep the heat down. That is sort of like locking a car in overdrive going up the mountain, it may do it but it working really hard when there is a much better "gear" available.
We are very hilly and it is normal for me to shift from high to low a few times a day mowing on my
BX25. kick in in low, do the steep hills then shift it to high for the fields. I even have to shift my 50hp on the big hills to a lower HST range if I am running the brushhog or something that takes power.