[doublesocket]

I think it's worth pointing out that whilst hydraulic limes have good breathability compared to cement, they are still inferior to "air" lime based mortars (e.g. hot mixed or made with lime putty). Although these have a slower set than hydraulic limes they are still in widespread use and a lot of straw bale construction will be using air lime as a superior alternative to hydraulic lime.

[bluGill]

In what way are they inferior? There are a lot of properties of building materials, and correct selection is about the compromise based on what each has. Cure time is one consideration, cured strength is another, R value, mass/volume ratio - and those are what I as a lay person can come up with: I suspect someone with more knowledge as a longer list.

[fartingflamingo]

I guess the parent commenter meant to say hydraulic limes are inferior in terms of breathability compared to hydrated lime. Which is entirely correct.

As always, it's a trade-off. Anecdotally, we did the base plaster layer on our straw bale house using hydrated lime for better breathability. We'll probably make the top coat slightly hydraulic using trass.