Curly natural hair is very limited in styles. I've had to accept this. I added bangs a month and a half ago just to have something different, and now I blow-out the bangs 2x a week when I wash my hair (just that small bit in front). It's the concession I made to have something change other than length. Well, I also added a lot more layering.
But if it's making you nuts not to have versatility than do a pro/cons in your brain. The pros of staying natural and with undamaged hair; the pros of flat-ironing. The cons of natural; the cons of ironing.
And consider alternatives--a different style of cutting, a shorter, not longer length (shorter can give a different look). Or products that elongate to simulate more length. Or rollers to have a style that's not fully curled, but not heat-damaged (you know, old style rollers, not hot rollers). Or a blow-out that's gentler for length. Getting length isn't the equivalent of stick-straight ironed hair. I have had blow-outs that leave my bottom wavy/curly and get a lot of length. I do that about 3x a year these days for a change (though I spent 1.5 years without a blow when I first went natural). Those moderate blow-outs were still damaging in a way, but less so, and they gave me 1 week plus of fuss-free, wake-up perfect hair.
If what you want is LENGTH and more FLEXIBILITY, you need to think outside the "flat iron" box. There are other options, from products, styling techniques, cutting options. Try the gentler options FIRST, before you cave to the blow-holes-in-your-hair-shaft consequences of ironing.
It doesn't have to be just a flat-iron, which is about as damaging as you can get. Why go to that extreme?
Try the non-damaging options FIRST, then keep trying until you find the versatility or lengthening you want.
But, ultimately, it's your hair. You wanna iron: iron. If that is ultimately what you really want--stick straight hair--then consider the options for that, too
Just accept the consequences. It's just hair. It grows back if you fry it to death.