I'm not sure if I understand you correctly. The point I'm trying to make is that a significant wobble in the star's position does not necessarily mean that the orbits around that star are very elliptical.
For example, consider two equal mass stars, one bright, one dark. These two stars can orbit around each other in perfectly circular orbits. However, a distant observer can only see the bright star which will appear to be non-stationary and 'wobbling' with respect to the background stars. Its 'wobble' will be as big as its orbit, but the two objects will still have perfectly circular orbits.
However, if you mean that such orbits are only detectable if the mass of one of the components is large enough to rival the mass of the sun, still, the sun-planet orbits can still be circular. But it is very likely that any smaller planet in the system will have a fairly elliptical orbit.
So if you mean that we can only detect systems which have a large planet component, and in those systems it is unlikely to find an Earth-like planet in a non-eccentric system, then I agree.
The real question is what is the relative abundance of systems with small planets and no large planets? Of that, we essentially have no data.
I didn't make the contrary assertion. What I said was that a significant wobble makes the system unsuitable for Earth-like worlds, and I stand by that. Either there's a super-heavy companion in some orbit, a heavy companion in a wildly elliptical orbit, or a heavy companion in a circular orbit of small radius. You can still have a small, rocky world in a stable circular orbit in such systems, but it will probably be outside the "life zone".