David,
It's hard to track because the spring training teams left right around the same time as the broader economic downturn was happening in Arizona and across the country. The White Sox left for Phoenix in 2009, which left just the Diamondbacks and Rockies there and led to them wanting out ASAP. They jointly built a stadium in Scottsdale and moved in 2011.
There's no doubt it played some role, but ultimately spring training is just one month out of the year and the munis are not the biggest market for that group of consumers.
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My general answer is that, in Arizona especially, golf was overbuilt and as the prices for CCFADs and resort courses has necessarily come down (and water costs go up) more play goes to those 'high end' courses vs the munis. When I lived in Tucson as a college student in the summer of 2002, I could play El Rio (walking after 4pm) for $4 (sure it was hot, but I was 21 and didn't care). At $4, I played El Rio and Silverbell pretty much every afternoon that I wasn't walking. Every once in a while I'd drive over to Randolph, which was a bit more expensive and busier. I think I splurged once that summer for a summer rate at Ventana Canyon.
Now, the best deal I see listed anywhere online is $18 but includes a cart, no indication of what they'd charge if I walked in this afternoon and asked to walk. At $18 I would not be playing multiple times a week as a college student. Ventana meanwhile is $35 for an afternoon round on GolfNow. So I might well play less but play at a resort like that or Dove Mountain and skip scruffy munis altogether.