The SWEs get called too, particularly if SRE isn't able to untangle timely.
Don't want to be called? Don't make incidents. Healthy orgs, as a peer comment points out, avoid too much separation between the positions. Things like change review are supposed to avoid this, but often gets rubber-stamped for 'velocity' (into a wall).
When they "work" instead of "make a giant fucking mess" its because SWEs take shifts as SREs and the distinction is more about time in the mines and less about distinct job functions.
In the original implementation, SREs have the authority to block further releases until the SLOs are green again -- and, if it comes to that, to hand the pager back to SWE until such a time the product can pass a production readiness review again. That requires a lot of trust on both sides, though, the building of which takes both time and deliberate effort, and I don't know how other shops do it.
Don't want to be called? Don't make incidents. Healthy orgs, as a peer comment points out, avoid too much separation between the positions. Things like change review are supposed to avoid this, but often gets rubber-stamped for 'velocity' (into a wall).