Obviously a RA would be done to assess the protection required but this will be balanced against cost.
That is if you are talking about professionally installed systems.
There not an intruder until they enter the premises.
Possibly, however there are chances of external incidents causing false alarms.
Bird strikes, window cleaners, post(wo)men, pets jumping at doors/windows, all this and more would need to be assessed in the RA.
Any detection of this type would need to be setup correctly as well this takes time, so therefore perimeter protection would be a lot more costly too.
Again, all down to risk and the customer. The layout of the property is also something to consider.
This would be a popular option on a low risk property.
Much better to have the downstairs armed than the customer feel "trapped" and not used the system at night.
Probably, again this would need an RA to determine.
With having animals you would have to install perimeter protection in some parts of the property anyway.
Ideally, I would install perimeter protection in addition to PIR's. If they get in somehow they could move around freely if you have not sensors in the rooms.
Another thing to consider is monitored systems, they will need two detector types in an area to trigger the police. Therefore, perimeter protection only would be useless in this instance.