IMO, it really depends on how serious you are. You can definitely play with just one cue, but almost no one does. The fact that all pros have a separate break cue (and pretty much have for decades) is probably an indicator.
In the "old days," I think having a dedicated cue was primarily so you didn't have to change shafts to break because you wanted a different tip (super hard leather or phenolic). [see Dr. Dave's advice:
https://drdavepoolinfo.com/faq/break/cue/ "It is best to use a dedicated break cue, which is beefier and has a hard tip (usually phenolic)"]. Folks also believed that a separate cue kept your playing tip from flattening out.
Technology has changed and we now have CF shafts, improved plastics, and also layered tips. I personally believe CF shafts improve breaking speed and consistency, although I haven't seen any empirical data on this. But, at least from a deflection standpoint they should help you break better. Layered tips mushroom less, so maybe that counsels against a separate shaft. Although breaking with an 11.8 might not be optimal.
**edit: Dr. Dave calculated phenolic tips provide ~17% increase in breaking power. So, just that change might justify a different shaft/cue for breaking.
https://drdavepoolinfo.com//technical_proofs/new/TP_A-30.pdf
All that said, if you are breaking 15-18MPH, there may not be a big difference between cues as your breaking speed/technique might be the limiting factor. But, when you start to break the balls at 23-25MPH, the increase in performance is more noticeable. And having a larger sweet spot for breaking can also improve the result at higher speeds.
-td (my $0.02; probably worth less though).
-td