In a way you are agreeing though, as you said, it took two months for you to be working on core services, so there is a significant ramp up time. If we are talking about a summer internship then it is questionable whether you will really add more value than extract. This is irrespective of ability level and just the reality of getting to know an organizations processes, codebase, etc..
In any case, I'm not quite sure what the article's beef is. If there was no market for unpaid internships, then there wouldn't be any. Clearly some interns are finding it worth their while enough to go work for free.
Do totally agree that it is an absolutely awesome funnel for candidates though, and worth drawing those candidates in via pay or other fringe benefits.
Having said that, I don't disagree - it definitely does have a rampup time and I don't disagree with that theres a market and value in unpaid internships, especially short term ones - I'm just saying that I also think theres value for employers and candidates alike in paid internships too.
So, interns are definitely not always a burden, but I certainly do understand that they often would be, but to be honest, you get what you pay for - if it had been an unpaid internship, I'd have had very little incentive to really put much effort into it. I mean, months of unpaid work would be demoralizing and I'd probably quickly have ended up producing little of value.. Luckily it never came to that and I ended up going back to work at the company for another 1.75 years, before I left to try out the world of freelancing and startups.
For the record, that company hires between two and five interns every year. They find it effective enough to keep doing it. They treat it as much as a hiring thing as a cheap labor thing and they find having (paid) interns to be pretty effective.