My space saver is the one that came with the car....so at least 2009! I've never had to use it but I would. To be honest I've never heard of anyone replacing a space saver tyre just due to its age!! But personally I like my road tyres under 5 or 6 years old....its rare they last that long anyway. And I change tyres over 10 years old on anything I buy regardless of what it looks like.....it will have hardened and wont grip anything like as well as a new one...even of the same tyre.. When I sell caravans I cant let anything go out of the gate with tyres over 5 years old.
Caravans are a bit different in that the tyres are almost always permanently exposed to UV and they typically spend most of the year standing in one position (with a lot of weight on them). Also you often only have two of them, so losing one is a 'bad thing' Hence I do replace my caravan tyres based on age (same with gas hoses, of course) ... even though I have Tyron bands and TPMS.
As far as cars go the tyres on a rarely used 2nd / 3rd car kept in a cool & dark garage won't age any quicker than spares do. But a low mileage car parked up outside in the open is a different matter.