Not that it directly bears on the question, but since it has come up a number of times in comments and answers, there is another aspect to the use of an escrow account to hold tax and insurance money during the life of the loan.
Before I address that though, it is not necessarily a true escrow service as the mortgage owner may use a third party as the above seem to suggest or hold the cash themselves, as the above also seem to suggest. Or the holder may be an "arms-length" subsidiary. Probably those are the main variations, but there could be others too. How "arms-length"? Oh, whole other company of course, though, um, the employees there have career paths in the mortgage owning company so... You can clearly see I am not bucking the tide concerning evil mortgage companies, but also not trying to shade a decent, honest one. "One" being the operative word, but...
However, the other important thing about this kind of escrow account, and really the large reason why a mortgage owner insists upon it when they can, is something that might be unique to the US, might not. That is that the PROPERTY owes the taxes, not the owner. If I default on my mortgage, and it turns out I didn't pay the taxes for, oh, 3-4 years, or one semi-annual payment, whatever, the property owes that money, not me. The mortgage owner takes the property and sells it, but has to pay the taxes before the competent tax authority will allow the ownership transfer. No one can force me to pay it, through laws, though obviously, they have a contract that they can enforce with some lawyer-type effort and collect via that: Say $100,000 is still owed, it auctions for $108,000 (lucky me, really, 'cause it could've sold for a lot less in an auction). They have possession of the excess $8,000 and will apply it as they feel the contract allows and I'll have to sue if my reading differs. If that does not cover all the costs associated, they lose unless their contract allows them further recourse. (But if it does, I'd've declared bankruptcy instead and ganked them for a lot more so...) All that drama aside though, no matter what, if the property owes property taxes, they cannot collect anything from the buyer (unless he's foolish) until those taxes are paid.
There is a different concern vis-a-vis insurance and that is the fairly obvious: If the house burns down, they want it covered so they have something to auction! Or you have something you want to keep paying for instead of walking away. For physical harm losses, like you pay some neighborhood kid to mow the lawn and he cuts his foot off and the parents sue you, well, if you have a huge amount awarded, guess what house is being auctioned off by the sheriff BEFORE the mortgage owner's concerns matter? Escrow is a way (there is another way, much preferred by owners) of ensuring that there IS home insurance. But as a practical matter, the most common way for it to come up is someone does not pay their insurance bill, a deadline triggers, and the mortgage owner gleefully forces their own insurance policy upon the property owner (by contract) and the escrow for insurance arises. If one didn't pay the bill to start with, it's likely one didn't have the money to do so and now the mountain is higher. I digress there, but that is how it usually arises.
The downside for the mortgage owner is it then is responsible for making the actual payments. Not a problem where the insurance (very profitable) is concerned, but surely onerous where the taxes are. The downside for the property owner is that if they screw up a payment on the taxes, it is he the sheriff's deputies are forcing out of the house, not the mortgage owner and where the insurance is concerned, it will only be enough to pay off the loan, not to replace the structure/s. The mortgage owner is the payee, and the property owner the beggar. Further, though the loan balance goes down, anecdotal evidence says the insurance cost never does even though the covered amount has...
So, no, not really escrow, definitely not really "true escrow" in the sense of an entirely impartial middleman holding the money, but it DOES address real concerns of the mortgage owner and so they insist upon it when they believe they can without losing the business. And even sometimes then.