As with anything, the general concept isn't necessarily objectionable. It depends entirely on execution. Courses with a two tee, two permanent basket set-up can work well if designed thoughtfully AND everyone playing is aware of the multiple set-ups and understands how they work. That's the troublesome part though...even with a good design, players are a wildcard.
But even independent of execution, the biggest reason that more courses go the multiple tee, one target route rather than multiple targets is cost. Whether it's rubber, concrete, or natural, tees can be installed for no more than about a third of the cost of a quality target. And when you're talking parks that have concrete readily available to them (and perhaps cheaper than retail) but not targets, that carries the day.
To piggy-back what JC said Mr. Billipo, another reason might be that rarely are there enough bomber greens (basket places) on any one piece of land whereas one can always place another tee somewhere along side a tree to effect a different challenge / different shot shape / length (than that hole's other tee). There just is usually a lot more decent / acceptable tee locations (using trees, etc.) than there are great green locations on any one plot of land.