I not only reuse rims but I reuse spokes. I've ridden more than 20K miles on wheels built with reused spokes. I haven't broken a spoke in 20 years; my wheels are true. But the cost is negligible compared to the time spent to build a wheel. I'm just lazy.
I used to have a 40-hole rear; that bicycle was stolen (at knife-point in NYC at the end of a ride from LA). I broke a spoke on it (fully laden, descending from Tioga Pass towards Lee Vining). I can't say it was stronger from my experience. Spokes are probably stronger.