@knotscott Depends. You should ask the fans, but one approach is to use a coaxial or coaxial-full range driver. If you are willing to accept the beaming above a certain frequency though you can get get most of the benefits of being without a crossover at all.
Yep - there's simply no "perfect" solution or approach to desgning full-range speakers. All have drawbacks. Some constraints are more important than others, and this is driven by how our brain / ear system, works plus add some variation for our differences as individuals.
If you want a more "perfect" approach you can try single-driver headphones - this eliminates the crossover, eliminates the room (you have ear interactions but it's "simpler"), and renders true full-range all from a single driver. You can pick your driver material - hard or soft - plenty good examples of both exist (I prefer soft). On paper, the headphone experience should be amazing. BUT, it's simply not as satisfying as a good speaker setup - even the really exotic and pricey headphone gear - and I've tried. There are multi-driver headphones too, and some of them are very good, even dating back to 1970's AKG K340!
The Tannoy coaxial (DC) is based on the idea that SOME coherence between the 2 drivers is necessary, but not 100%. They're phase coherent, but only precisely at the crossover frequency. They are NOT time aligned. Their 15" woofers are probably beaming at the 1.1kHz crossover (even worse for the 15" tulip waveguide models at a higher crossover frequuency), but the horn tweeter helps cover for it, and at least the radiation pattern is symmetric (coaxial arrangement). IIRC there was a study that claims human hearing can appreciate the affect of EITHER phase coherence OR time alignment, but that having both netted no additional benefits. The brain is wild, man.