"devices that use significant amounts of power nowadays have to have additional components to bring the power factor down to close to zero before they can get a CE mark in Europe" (did you mean close to 1?)
"... no longer anything resembling a sine wave"
The CE people are still on the case. In recent years, CE marking done properly (which is a topic in itself) requires that equipment does not make any significant contribution to harmonic currents in the mains.
So in principle, recent appliances with CE marks should have power factor close to 1, regardless of whether PF means current and voltage phase relationship, or whether PF relates to non-sinusoidal current waveform.
YMMV (your meters may vary).
If you have time to spare, some enlightenment is available (including limits on what level of non-sinusoidal current is classed as "significant"), e.g.