The limitations are for normal operations, not emergency circumstances
Actually, the limitations are for both ...
The basic structural, handling, performance etc., qualification of the aeroplane is based on limitations as these provide the fence around the paddock.
Fatigue and planned maintenance considerations are based on a presumption as to the way the aeroplane is going to be operated. If the aircraft routinely is operated less conservatively than such presumptions then one anticipates observing an increase in costs associated with routine maintenance activities. Indeed, if one considers structural fatigue, there has been a number of cases of wings falling off in flight as a consequence of this very point ...
One would be VERY wary about, and careful when, exceeding limitations during emergency procedures ... unless you definitely know that, by doing so, you don't create a bigger problem (generally you won't and can't know this) ... and, at the end of the day, the FDR etc., will catch you out at the enquiry ... be very prepared to defend yourself against some searching questions in respect of acts/omissions which might be indefensible at law.