That's a non-sequitur. Yes, orbits in reality are probably going to have some small residual eccentricity if there isn't anything else there to keep it forced at a higher value, but it can still end up so small that there's no tidal heating. Triton - Neptune's big moon - originally must have had a high eccentricity when it was captured but its eccentricity now is 0.000016 (which is VERY low in solar system terms - even the orbits of the innermost asteroidal moons of Jupiter - which are subject to a lot of circularisation - are more eccentric). You can see the effect the tidal heating had on its surface in the Voyager 2 images - huge areas are resurfaced completely - but that heating isn't happening anywhere near as strongly anymore because the eccentricity is so low (that said, Triton's inclination is pretty darn high, but I don't think heating resulting from the orbit moving into the equatorial plane is as bad. I am admittedly a bit fuzzy about that).

But that has nothing to do with our moon raising tides on Earth as it moves around it. That happens because the moon's orbit is eccentric and the earth is rotating. But when the moon's orbit circularises, and the earth becomes lock to the moon (which won't happen for billions of years, if we don't lose the moon from orbit altogether before then) then the tides won't happen anymore.