The crossover isn't just used to separate the frequency range into base and treble. It is also used to iron out any deficiencies or make adjustments to how the speakers sound. The impedance can also be "normalised" in the crossover too.
8ohm impedance speakers are a nice easy load for any amplifier. But most drive units are 4ohms impedance, so the crossover is designed to present an 8ohm load to the amplifier, but to do that means more components on the crossover, which generally degrades quality - so you're sacrificing quality in order for the speaker to be friendly to the budget amps they're likely to be partnered with. This is why better quality speakers generally have a lower impedance, because less is done in the crossover to counteract their natural 4ohm characteristics, which retains their inherent sound quality. I was quite surprised to see a sub £1000 floorstander from a well known manufacturer recently that are 6ohms, but dip to 3! Most people are going to partner those with a £500/600 amp, and they're not going to handle 3ohms - you'd need spend a good £2k or more to get something stable at that impedance.
The sensitivity of the speaker will depend on many things, including the amount of drivers or surface area of the drivers. Speakers with more drivers or larger single drivers are shifting more air, so need less power to match small speakers. A sealed or ported cabinet will affect efficiency too, with ported cabinets being more efficient, but they have their trade offs. Horn loaded speakers are usually quite efficient, but for many have a sort of "shouty" quality, as they focus higher frequencies quite strongly towards the listener.
Designing a loudspeaker is a massive balancing act of many things - change one thing it affect another, and correcting that might effect sound quality or efficiency etc etc.
This is why system building is still an artform in many ways, but people seem to just throw things together willy nilly nowadays (I guess with the nature of the internet and easy online buying), which I feel is why there's so much second hand stuff on the market. They order something without auditioning or seeking the right advice, try it out and decide they don't like it. They probably would like it in a well matched system, but it's just not able to shine in theirs because it's not playing ball with something else - much like the Rega and Elacs in your case. I can see that in the specs, but having experience with the Elacs, I guessed straight away what it might be.