I don't escrow, so I don't have direct experience here, but another limitation of escrow would be using property taxes to maximize federal tax deductions. With escrow, I assume you have no choice but to pay the property taxes on time at the end of the year. Without, and assuming you basically skirt the standard federal deduction threshold every year, you can come out ahead by paying 2 years worth of property taxes in one tax year, itemize deductions, and claim a deduction above the standard, and then in off years when you pay no taxes, you claim the standard deduction. Overall, you come out ahead. Some numbers as an example: $5k property tax, and your other deductions come out to $5k per year. So each year, you have $10k of deductions, below the standard deduction of 2015 for married filing jointly of $12,600, so each year you take the standard and don't itemize. If instead you pay 2 years worth of property taxes this year (prepay 2016 along with 2015's), you now have $15k worth of deductions for 2015, so you itemize and taken a higher deduction/pay lower taxes. Then in 2016, you only have $5k of deductions (since you aren't paying property tax that year, it was prepaid in 2015), and therefore you take the standard deduction of $12.6k. Assuming the numbers stayed the same (they won't), you would average $13.8k of deductions a year rather than the standard $12k.
It's not a lot of money, maybe around $100-300 a year tax savings depending on your actual numbers, but it's something to consider. This of course doesn't even get into the opportunity cost loss of prepaying taxes, but if you were cautious enough not to want to invest "next years" taxes, this is a way to get a small guaranteed return.