White bread is super processed. Speaking as someone who eats a mostly whole-foods diet, I never touch the stuff. I wouldn't balk at feeding it to my chickens now and then, but I'd consider it junk food and would avoid giving it daily. But you know, I've also said in posts that feeding chickens leftover pizza is not a big deal, provided that it's an occasional treat. But for the core of their diet you really need to have something more nutritious and ideally more variety.
No you definitely don't need to buy expensive formulated layer feed to keep your chickens healthy. In our grandparents' time people fed chickens mostly on scraps from their kitchen, but those scraps would have been a) mostly whole foods, not the processed cr*p most people keep in their kitchens today, and b) a wide variety of different types of meat and produce, not just primarily bread scraps. Chickens are a lot like humans; they need a varied diet, adn the more diverse their sources of food, the easier it is for them to get all the vitamins and minerals they need.
If you're looking to save money, there are better ways. For example, you can buy a few grains in bulk and mix your own, and then add a tiny bit of vitamin supplements (I like Fertrell Nutri-Balancer, for example). You can ferment feed which makes it more nutritious and last longer (super easy - just soak a bucket with a few days worth of feed in water overnight). You can hit up local grocery stores (try the smaller ones, not the big chains) and ask them if you can have their "expired" produce that they would normally throw out; just tell them it's for livestock because they're usually legally restricted from offering "expired" foods for human consumption. You can let them free range so they get plenty of bugs. If you want to think long-term, you can plant some fruit and/or nut trees and let them forage under them.