Seemed inevitable but: convert tidal energy into electrical energy and you rob the Earth of angular momentum. This in turns leads to other climate problems over a thousand years but climate problems just the same.
Granted that all energy conversion to electrical energy is somehow robbing Peter to pay Paul. It's just a matter of which Peter is being robbed and how deep his pockets are.
I'd rather have a thousand year horizon for developing alternatives than our impractically short current trajectory. However, this study also cites impact from tidal energy use in the near term. Sadly, TL:ADHD beyond the abstract. https://cs.stanford.edu/people/zjl/tide.html
@elight this article points put that global energy usage has increased by about 3% per year over the last 50 years, and assumes that that rate of growth will continue for the next 1000 years. So, 3% compounded for 1,000 years. Long story short, the article assumes that in 3023, we will be using about 6.87 trillion times more energy than we used today. A lot of the secondary math might be right, but I think that initial assumption is unlikely to hold up
I think your strategy of taking it 100 years at a time is solid, but rather than calling this paper hard sci-fi I think it's closer to an object lesson about the dangers of applying pure math to an engineering and economics question.
The strategy of "Consider the trends of the past century, and assume they hold for the next millenia" has never been an effective way of predicting the future