If you opt for drivers being small compared to the wavelengths emitted, and a comparably slim baffle, a wide directivity speaker is actually pretty easy and cheap to build. Take a 6.5" woofer, a 2.5" midrange and 0.75" dome, choose low crossover frequencies - voilà!
Is this a desirable concept? For home listening, rather not. Wide dispersion usually comes with higher SPL being radiated towards ceiling, floor and side walls, resulting in dominant early reflections and degrading localization. For nearfield monitoring in a well-treated studio, it might be an excellent solution, though.
That is really the one thing that is difficult to implement over a vast frequency range. Not impossible, though, as Duke has mentioned. An adjustable rear-firing tweeter (plus upper midrange if necessary), would do. Sonus Faber has done something like that in the past:
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Such concepts are usually resembling adjustable bipoles in the treble bands, but their sound is heavily dependent on how reflective/diffusive the rear wall behind the speakers is. I guess that was the reason why SF have implemented a mechanical possibility to alter the horizontal angle of the rear-firing unit.
Note such are concepts to widen directivity hence reducing directivity index. Adjustable directivity concepts to narrow the beam, such as the Beo 90, are much more complicated to design and usually involve driver arrays, which I would recommend for tweeters.