Someone can correct me if I’m wrong, but I don’t believe there have been any actual studies that have proven the benefits of breakfast. Most of the studies done are either on a very small scale or they are just observational studies - people who eat breakfast are shown to be “more likely” to be healthier than people who don’t, mostly because it shows an increase in activity. People who eat breakfast tend to get up earlier and are shown to be more active. But if you’re already healthy and active, breakfast hasn’t proven to be better or worse.
If eating breakfast makes you crash, I don’t see how it will help you.