I was debating this - the psychoacoustic "evidence" on preference for or against omnis - at another forum some time ago. When I looked into the research, I saw that omnis have fared very well in all the experiments I could find where an omni was compared to a dipole or a conventional forward-firing speaker.
Flindell 1991 and
Bech 1994 were direct comparisons of omnis and other designs (but Bech doesn't discuss it himself, his data were re-analyzed by Evans et al
in 2009). In Flindell's study naive listeners preferred omnis, while professional listeners found the omni and the conventional speaker equally good. In Bech's study, the omni and the dipole came out on top. [edit 05.01.21: with positioning out from the walls]
As mentioned in the thread, the almost-omni Mirage M1 scored higher than any other speaker at the NRC in Canada during the 80s, so much so that dr. Toole chose it himself. [edit: it is actually rather bi-directional, not fully omni]
Choisel 2005 did a comparison of a conventional speaker with the Beolab 5, which is semi-omni [edit: or rather has
very wide dispersion horizontally], with regards to imaging. Beolab 5 imaged as good as the other one. This text isn't available online, but the results are discussed in depth in dr. Toole's book.
David Clark did
extensive blind testing in 2010 of three speakers, the dipole Linkwitz Orions, a pair of cheap Behringer monitors, and "The Imp", a DIY quasi-omni speaker by Gary Eickmeier. The outcome of interest was "plausibility of the auditory scene", and the DIY quasi-omni came out on top.
I'm not aware of any other blind test of omnis. As said in another thread, preference testing of loudspeaker designs is not a very big scientific field. But the studies done so far certainly don't indicate that the average listener has any aversion to omnis, when they don't know what they're listening to.