Unless I'm reading this incorrectly, the audit shows that the effective tax rates for FY13/14 are the lowest they have been in the last 5 years (page 6). So in some ways it looks like they benefited from decreased property taxes, though that audit was completed about a year ago and I'm sure oil has hit them pretty good. The audit also anticipated a decreased budget for 2014 despite a successful economy.
Overall, I understand your position but I don't think this particular tax cut is a cause for concern. The tax cuts proposed would only affect residential property I believe not businesses (in fact businesses are lobbying because they want tax breaks too), so the affect would be minimal considering businesses pay the majority of the property tax revenue. The bills that I mentioned previously would only affect provisions for how cities conduct their tax revenue calculations and elections, not direct lines to their budgets. Those bills have also failed in the Texas senate apparently over the last 30 years (doubtful it would pass alongside the tax cuts). This is looking to be a win (not by much) for home owners and individual tax payers. Yes, I agree that in general things should be left to the individual cities and I don't necessarily support the measures. Though I see why they might be considered.
I even reached out to a local contact for an economic development corporation in one of the boom towns and asked about his take on the matter. He didn't even know what I was asking about.