Hello Navi
Yes, some native speakers do use the present progressive form, either for emphasis, as you say, or during the period of "having to" itself, as here:
Ex. 1
"What are you doing with MrQ's report? I thought it was finished."
"It's full of grammatical mistakes. I'm having to go through it line by line and correct it."
Unfortunately, some grammar books for
ESL students ignore this usage, or present it as somehow ungrammatical.
MrP