[Symmetry]

I think if we're positing a world where our energy use increases 2% annually for a thousand years and that tidal power will remain a fixed fraction of that we're not dealing with a reasonable projection. In any event, at the end of those thousand years humanity won't be very far from Dyson Sphere territory and the tidal locking of Earth wouldn't be much of a problem for the civilization implied, but I don't think it's possible to extract tidal energy that fast.

[stouset]

If the world’s energy use increases by 2% annually for a thousand years and we’re generating it with anything other than wind/solar/tidal/geothermal, we will raise the equilibrium temperature of the Earth by tens of degrees just from thermodynamics.

[CorrectHorseBat]

If the world's energy usage increases by 2% for a thousand years we use 3.4 * 10^4 times more power than the solar radiation reaching the earth (1.02^1000 * 15/170000). Enough power to boil off the oceans in about a day (if I can believe Reddit and my math isn't off)

[stouset]

Yeah, I've done the calculations for 3% at 2%. I didn't feel like doing them again, so just went with a conservative bet.

[Symmetry]

Nah, to keep extracting the Earth's rotational energy that fast through tidal means we'll have had to import all the available liquid water from the rest of the solar system, rendering the climate change effects of the other energy use moot. ;)