I'd be impressed that a small child can sit still that long tbh.
I think YABU about the straightening - it won't permanently damage her hair, hair grows, it is cut, it grows some more.
I'd be interested in knowing the context though - if its for fun, for messing about, for a change, for her to experiment with different looks - fine, that is surely as normal as other hair styles, dressing up etc.
IF there is any 'i HAVE to have straight hair to be pretty/attractive/be friends with a specific person' or 'my natural hair is wild/messy/untidy and thats bad'.. then yes that is a problem.
I desperately wanted straight hair as a kid, I had absolutely wild curls, my hair used to eat stuff.. and I had no idea how to make the best of it or what to do with it and my bloooooooody mother brushed it into oblivion and a frizzy awful mess as she had no idea either.
I think if I'd been able to play around with straightening it but also, been taught how best to manage curly hair and what worked with it, I'd have been far far happier, but I was mostly bullied into having it cut short as it is 'so unruly and wild and scruffy'.. ugh!