My original mortgage had tax escrow (no insurance escrow), which I didn't particularly care for (especially when they initially neglected to pay tax on both parts of double lot), but as a first time home buyer probably had no choice. At least when it all shook out and they sent me too much money back, and then needed it to make up a shortfall the next year, they gave me a long time to pay it without interest.
When I researched refinancing a year or two ago, internet info showed higher interest rates without escrow than with. When I refinanced with my existing lender 3/05 (effectively a 1st lien HELOC at $170 closing cost for lower fixed interest/shorter term), I was thrilled that they gave me an interest bearing checking account to do my own escrow (to auto-pay loan, and write my own checks for tax/insurance).
Now that I pay my own taxes, a different problem. County website shows 1st installment tax "unpaid" plus interest, e-mail to treasurer said no record of mailed payment, but my check (with correct tax account numbers) has already cleared and was deducted from account before the due date. So that needs to be resolved.
Where some people get into trouble, even with escrow, is when they buy a newly built home, initial taxes due from previous year were for an empty lot, the lender underestimates tax for completed home, and the home owner suddenly ends up with much higher escrow payments than expected (double annual tax) to make up the shortfall. That along with rising variable interest rates could really take a bite out of a budget.