The problem is, to even reach the comet, you have to achieve that speed already by other means - but once you have reached that speed, the relative motion of the comet is 0 m/s.
There is actually something like what you might consider, only a little different. If you fly towards a large mass (like a planet) you can use some of the planet's momentum to accelerate your spacecraft if you plot your path carefully.
That is already being done for a long time and is called gravity assist - in fact the Rosetta mission you describe did it multiple times. The problem is, that you need a huge mass to assist you (a comet would likely be too little) and it needs to travel in the right distance at the right speed at the right time.
Oh and btw. Earth itself moves around the sun at 30 km/s. The speed noted in comets is either orbital speed (wich is similar to Earth's speed itself) or speed towards or from Earth. So the comets usually aren't that much faster or slower than planets anyways.
As for interstellar travel, 70 km/s might sound very fast, but compared to light speed, it is only a small fraction of 1/4285 c. So the nearest star system (Proxima Centauri) is still 18'425 years away at 70 km/s - and only that if those comet is rushing directly towards Proxima.