Like virtually any engineered product, there are an endless series of tradeoff decisions to make when designing a speaker and deciding on 2-way versus 3-way (or more!) As others have noted, transitioning from one driver to another affects the sound quality in that frequency range. The ear is particularly sensitive in the bandwidth in which most instruments (including voice) have their fundamental range -- roughly just under 100 Hz up to about 3,500 Hz. Some speaker manufacturers try to avoid switching drivers in this range. However, if you try to use a large driver (to preserve bass) you'll end up with beaming in the upper range of this band. Using a smaller driver addresses this issue, but makes bass response more difficult.
And these trade-offs go on and on in lots of other areas. Ultimately, all you can do is audition lots of speakers and see which make and model best lines up with your own preferences.
Or, you could do what I did and end up with a set of Ohms. They use one driver for bass up to around 8 kHz and only cross over to a tweeter at that frequency. But, they have their own compromises since they have a semi-omni radiation pattern, which some love and others don't.
So, the advice you get here may give you some interesting candidates to check out but ultimately you should ignore the rigid advice others give and just buy what sounds good to you.