I can't give any personal insights here as I haven't had to particularly scrimp. But the overall thru-hiker culture is pretty frugal (if not sometimes beyond frugal), and that sort of rubs off. I think even a really rich person who normally lives a carefree spending life would find themselves acting pretty thrifty just because that's the culture everyone finds themselves in --- cramming multiple people in a motel room, that sort of thing.
The "start later" suggestion certainly makes sense. I would add the caveat that a good way to keep your food costs down is to start with or perhaps just after "the herd" --- so that you can maximally reap what's left in hiker boxes. This is particularly true early on, when folks are typically mailing a lot more food to themselves than they can consume, but to some degree it's true throughout. I hiked with a guy for a while in Oregon who was on a super tight budget, and if he found a well stocked hiker box he would walk out with 8 days of food even if the next resupply option was only 2 - 3 days away. As an aside, one can debate the morality of cleaning out a hiker box because your own budget is arguably insufficient --- I don't mean to get into that, other than to suggest that you think through it and feel your way to the best behavior for yourself as you go along.
The thing that's tough for people I think is that you have a great chance of hiking with other people and enjoying their company. It could be very unhappy to see them going into town to zero, shower, relax in a motel room and eat burgers while you grab the cheapest food you can get and hit the trail again. Equally unhappy in a different way is if people come to see you as a leach, trying to sidle into the motel room they paid for at low or no cost or gazing with puppy eyes while they open their resupply boxes from home.
I'm not saying that you can't hike a long trail on the cheap. I do think that for the *average* person it's good to have (in today's dollars) something on the order of $4000 set aside, not counting what you need to get to and from the trail in the first place, nor anything for health insurance or unplanned emergencies of whatever sort. Trying to hike the trail for less than that requires compromises that you really can't grasp, I think, until you have been hiking for a few weeks.
I guess the one saving grace is to realize that it's not the end of the world if you can ultimately hike only part of the trail before you run too short of funds. And that all the thru-hikers around you look, smell, and sometimes even act like hobos too! :-)