That’s not really practical. For a lot of on-call roles, you need the experience of working on the equipment daily to know how to fix it.
Even if you alternated e.g. a week of on-call then a week of normal shifts, you end up reducing the amount of time you have that is completely non-work.
Firemen are absolutely not doing nothing until called out. There’s training, maintenance, cleaning, post-incident paperwork, and probably other duties.