You can always ask for a cup of water for free at quick service restaurants. They don't make you pay for a bottled water (not being snarky, just letting you know because I know there really are places outside of Disney that won't give you a free cup of water when they have bottled). You are right about the lines during peak times though. Having your own bottle would be more convenient.
Cost is not an issue. Time is. We are going the week of Easter this year. That said, it is highly likely that I would pay $5 for a water to not wait in line for more than a couple of minutes. If I bring my own water, I can save valuable time and money
