Assuming you are a native Hebrew speaker (like me), I can see why you'd say that, but it's debatable. If you you want to speak "proper Hebrew", or want to write it in a newspaper or a book, then בא vs. מגיע should be pretty much like "come" vs. "arrive" in English, and here it should be בא. I believe that several decades ago all Hebrew speakers would speak this way, too.
In recent years מגיע has been gaining ground over בא by Hebrew speakers (for "come"; בא has been gaining its own ground over other words in different meanings...). So now indeed you're more likely hear האוכל מגיע. But I hope it's not yet a sweeping victory. FWIW I would still say האוכל בא - at least I hope I would, I could be misleading myself...
There is no technical problem with saying "אוכל בא". The problem is contextual and it might not be understood, and sounds extremely awkward on its own. Here is why: Hebrew has no 'progressive' tense (like most languages), and it is derived from the context.
So if you translate to English, "האוכל בא" would like "the food is coming" (although also awkward, as I pointed out in my previous comment), while "אוכל בא" would be more like "food comes". You can see that even in English, saying this separately without any context would be extremely strange.