The question of whether this trope is Truth in Television is a complicated one. It certainly can be painful to wear a corset, but it doesn't have to be, and isn't always.
In general, there are four factors at work in whether wearing a corset is painful or not. They are
- The design of the corset.
- How well it's fitted to the person wearing it.
- How tightly it's laced.
- How accustomed the person is to wearing that style of corsetry.
Many people in the corseting community take comfort and safety very seriously. When fitted, made, and worn properly a corset should never cause any pain.
The design
The shape of corsets has changed radically and continually over the centuries, as the "desirable" female silhouette has changed, so corsets from some eras will be inherently more prone to be uncomfortable than others are.
How well it's fitted to the person wearing it
Do you know how most actresses complain of how painful it was to wear a corset for a period role? It's likely because of this. The speeds and demands of film work mean that costume designers can't spend days or even weeks properly fitting a corset to a person, and like a bra it can mean massive discomfort.
How tightly it's laced
This can also contribute to modern actresses hurting in corsets. Since corsets haven't been a part of regular fashion since WWI, most people don't know how to properly lace a corset. There's also the stereotype that corsets necessarily hurt, but if it's painful the sensible thing is to loosen it as people used to do.
It's heavily overestimated. A modern eye might be tempted to look at the wasp waists and imagine that what the Victorian doctors said
must be true, that tight lacing claimed an unimaginable number of lives. The reality is that, since you're likely looking at a photo or drawing, the figure was exaggerated through other means aside from corsetry.
note And no, nobody ever had a rib removed so they could lace themselves tighter — not least because surgery in the time when corsets were prevalent was an incredibly dangerous proposition that was quite likely to end up with the patient dead. Artists produced the ideal and not the factual, and people still managed to photoshop their photos through black or white paint — photo manipulation is as old as photography itself. There's also plenty of padding at the hips and bust to give the illusion of a smaller waist.