The fainting woman trope is often used as a literary tool far more so than a historical reality. It's a very easy way to show the woman as the standard damsel in distress, frail and in need of masculine assistance.

Unfortunately there is a stigma for this today that really isn't true. The modern belief is that corsets, stays, or bodies (depending on how far back you go) were restrictive to the point of not being able to breath properly. I'll agree that if someone who never wore a corset or other supportive device put one on they would feel some discomfort to begin with. However, if properly fitted it should not constrict. Tight lacing was as extreme as 6"+ stilettos today. We laugh at women trying to function that way. It was much the same for women back then. Sure, extreme fashion could be an option, but they literally could not do what they needed to do at work or home. As an everyday woman my garments have to allow me to go about my daily business- and breathing is a part of that.

As someone who personally wears historical garments on a regular basis I can attest to being fully functional in a corset or stays (i.e. pitch a tent, ride a horse, sing opera, muck out a pig pen). In fact, it fixes a medical back issue I have that doesn't allow me to stand or sit for very long. What does sometimes cause "faintness" to occur is when I'm wearing a heavy garment on a hot day or spend too much time in the sun, but most women would be smart enough to dress for the weather and wear a hat.

Women did faint more then, than now. But then=100+ years ago, not 60+ years ago. The difference is relevant, because the reason so many women fainted was that the fashion back then was to wear extremely restrictive corsets that prevented them from taking deep breaths and also restricted blood flow. It was therefore easy to faint at any stressor that would normally cause someone to breathe more deeply or get excited in some way. Women routinely carried smelling salts with them to aid in waking up after a faint. Homes had fainting couches to rest fainting women, or women who felt like they were about to faint. Historical re-enactors and modern actresses starring in period pieces have confirmed the increased likelihood of fainting when wearing restrictive corsets. Such corsets faded out of fashion in the 1910s or so, and so the fainting spells were minimized. Though being very hot or dehydrated or hungry can also cause fainting, and those issues still exist. With the advent of better nourishment and air conditioning and readily available water in the 1st world at least, those causes of fainting have been reduced, too.

So yeah, lots of fainting in the 18th-19th century. But writers could also have used artistic license to have women faint at the most dramatic moment possible to the story. In real life, fainting was unlikely to be so exactly synchronized with the demands of the plot.