According to A Dictionary of Intermediate Japanese Grammar, under the には entry, には can take a noun if it's a noun of action (third paragraph). には is に + は after all, so I assume that the same rule applies for just に (they're not that specific). If so, I don't see how 朝ごはん is noun of action. This is the only sentence that I've come across that doesn't follow this trend, yet it's said to be the purpose particle に in The Japanese Stage-Step Course.
Indeed, that explanation ("に functions to express the purpose of an action") seems misleading to me. 朝ご飯 is a simple noun, and 朝ご飯する is ungrammatical. Here, this に is a rather simple role/purpose marker described in several previous questions. It roughly corresponds to "as" or "for" in English.
- に to indicate the role you want something to play?
- Meaning of にと思って in a sentence
- Can に have the same function as として?
- grammar of 前の誕生日プレゼントにもらった彼女の絵
に can also take a suru-verb as a purpose, for example 運転には免許が必要だ ("To drive it, you need a license"), but your sentence about 朝ご飯 is slightly different.