It's all about whether benefits of taking aspirin outweigh costs / risks.
Risks of taking aspirin can include gastric (stomach) bleeds, which can cause anything from anaemia to death. Costs (financial) are negligible, as aspirin is one of the cheapest of all medications - so cheap that it costs many times more to NHS to prescribe & dispense than it costs to buy over the counter(less than ?1.50 for 100 dispersible 75mg tablets, a bit more for enteric coated).
Benefits are reduced chances of heart attack and stroke. But if your wife has low risk of heart attack / stroke, then reducing a low / very low risk to even lower, may not be necessary. Being female and not having diabetes makes her lower risk than Austin Mini, although she may have other risk factors eg family history, smoking - I'm not assuming anything, except that GP has probably used risk analysis charts for both of you