I'm just taken back to a time when I ignorantly applied for an intern job to learn what I had little to no knowledge about. I imagined I would try to learn as much as I can so I could have the experience, the recommendation and knowledge gained if I am selected to intern for the project.
At that point, I didn't even bothered about the "no pay" in the description because all I needed at that point is, gaining knowledge and experience to do a job that I'll get paid for. I remember it was a 6 months long internship and even though it seemed too long, I still wanted it for the benefits.
To cut long story short, I wasn't selected and I wasn't pained about it since it was going to be an internship with no pay after all. But deep down, I'd have loved the experience that would have come with it. Applying with those thoughts and being rejected taught me something for this prompt.
Internship, in its simplest form, is about gaining experience and knowledge using the real world as a playground. You get to gain real life experience on a job that you admire but have no real experience on aside theories. So firstly, you shouldn't apply for an internship if you want pay.

The purpose of applying for an internship should be clear, that way, you won't feel like you're being exploited when the company make you do activities especially if they were all in the description of the internship opening when you applied or was stated clearly during the interview.
I know of internship programs that do pay their interns and it is stated clearly from the beginning of the internship opening. For those kinds, I think the company or project owners are being generous because internship experiences have helped many people gain good jobs afterwards.
I think the exploitation is happening on both ends when an internship is set as unpaid, the company provides the intern experiences on their expenses and the interns are taking tasks off the company for possible profits by doing real time work. At the end, both have gained something.
For me, I believe deciding if a company should pay an intern or not, depends on the kind of internship, the location and the worth of experience to be gained at the end of it. The intern applying should know what it entails and the company should be clear on what they offer.
So it is easy that in the process, when the intern seem to be doing more than was agreed, they can say they are being exploited and the best option after that realization is to leave. No company should exploit an intern but if it was clear on the description before the contract was accepted, interns know what they stand to gain.
Image used is AI generated.