Good drivers with uniform frequency response and low distortion are not cheap. Good passive components are not cheap. By the time everyone gets their markup the sticker price can be 10X what the components cost. Ergo for some definition of "affordable" and "high-end" affordable high-end speakers are 2-ways.
Good (expensive) drivers are also often useable over a much wider frequency range - tweeters with low resonant frequencies can be crossed over lower, mid/bass drivers with low inductance and phase plugs work well higher.
The best midrange I've heard from a dynamic driver is with an 8" Seas Excel in a 3-way configuration. It's at least in the same league as ESL midrange, although I haven't listened to that recently enough to pass judgement.
However, bass _will_ cause midrange IM and doppler distortion in 2-way designs, especially with smaller mid-bass drivers. A sub-woofer with an 80Hz high-pass (preferably 4th order) works _wonders_ to fix that.
You might look at your source.
If by Yamaha amp you mean a receiver, it may have problems with the 4 Ohm loads at high levels.
You may just not (yet) like your speakers.
Break-in is mostly listener break-in, even on speakers. You will get used to the sound and not notice inaccuracies until you compare it against a live performance. Different sounding speakers will sound wrong in comparison. Similarly, your old (broken-in) speakers will sound wrong if they're sufficiently different from new speakers you've lived with for a few months.