A local arena/public gathering spot for entertainment isn't the worst thing they spend money on.
It might not be the literal absolute worst thing to spend money in, but it's close.
It produces the wrong kind of jobs that a city wants (mostly part-time and low wage jobs), it doesn't boost the construction industry at all (studies have shown that it doesn't create new construction jobs or projects, it just diverts resources from other projects that either get delayed or cancelled), and the limited beneficial effects have shown to be very up-front and not sustainable over the long haul (large benefits for the first 2-3 years after constructuion, dwindling every year thereafter).
There was a poll where something like 86% of economists were either "against" or "strongly against" civic subsidization of professional sport stadiums. Only about 5% of economists were in favour. And this was back in 2006, before construction costs balooned wildly out of control over the past 5 years or so.
We've had the discussion on these boards over the past few months. Lots of good studies out there that definiteively suggest that it's one of the worst civic expenditures from a purely economic perspective you could embark on.