Im narrowing this question down to the main left and right speakers and ignoring center channel, bipole and dipole surround speakers. My thinking is that a good speaker is equally adept in performing both 2 channel and main left and right speakers in HT equally well. If its better in one role than the other, can it still be considered a good speaker? What say you?
Broadly speaking, that is true. But the details get a little more nuanced.
Presumably a two channel system is two speakers, intended to reproduce the full range of the recording. That means they need to play into the bass region well, typically at least 40 hz, and ideally lower. To achieve this, designers use ports and or other design choices that extend frequency response into the bass -- but at the expense of over all efficiency, and sometimes at the expensive of linearity.
A home theater system, on the other hand, is traditionally bass-managed -- meaning the left and right speaker don't need to play much lower than 80hz in most installs, since the bass can be better handled by a set of subwoofers, correctly set up.
This difference allows for a much more efficient speaker design. It can be sealed, as well, allowing for smoother integration with the subwoofer, and none of the minor (but real) challenges of using a port.
So while it is definitely possible to design a speaker that works great for home theater and two channel usage, you will be "wasting money" in the sense that you are adding in a lot of bass extension to a home theater speaker where is doesn't need it, and greatly reducing the efficiency of the home theater speaker by doing so, greatly increasing the power handling needs of the speaker for home theater usage, and thereby increasing you amplifier needs (more expense.).
Each person will need to make their own decisions about how to handle this situation.
For me, I chose great home theater speakers -- excellent linearity, good efficiency, not ported, and the bass rolls off a little below 80 hz -- because I prefer to control room modes with a multiple sub setup, anyway. I get full range two channel reproduction, but use more than just two speakers since I am also using dual subwoofers, set up in mono, time aligned with one another (sometimes called phase-aligned) and then time aligned with my mains:
https://open.substack.com/pub/hometheater/p/coming-soon
