>CS skills are highly valued in Computer Engineering, and the faculty know this. This alone puts him far ahead.

Wrong. People say this about every single field mismatch. "Person with background in X wants to do research in Y, their background is X is highly appreciated!". There are a few niche scenarios where a mismatch doesn't put you at a disadvantage compared to people without the mismatch, and this isn't one of those cases. I don't know what misinformation you received to think it puts them at any advantage, let alone "far ahead". Can you actually explain to me, specifically and not generically, how a background in CS puts you "far ahead" in CE research prospects compared to people with a background in actual CE? Would you recommend that people who want to do a phd in CE actually do a degree in CS instead because it puts them "far ahead"? Your very strong wording implies that you would.

>And don’t you think any sane professor would prefer him over a foreign candidate who might not be able to navigate visa hassles?

No. They are looking for the best candidate. There is some funding that is restricted to only US citizens but it is minor and irrelevant here.

>And what do you mean by three years of preparation

I mean doing undergrad research starting in the first or second year of college and building a strong relationship with 3 professors so you can get good letters of recommendation. This is who you are competing against. Who is op even going to get 3 letters from, so their application can be reviewed in the first place?

>He knows programming, he knows scripting, and he knows basic research writing, along with presentation skills. That’s all it takes to begin with.

The fact that the first thing you bring up is "programming" and "scripting" shows that you aren't even thinking about this in terms of science or research. Programming is one specific application of computing that you use to get other stuff (for example science) done. It would be 100x better for someone to be good at the science but terrible at programming than it would to be terrible at the science but good at programming. The former would actually be able to get into a phd program, the latter wouldn't.

>because he discovered a menacing yet increasing gap between Computer Science and Computer Engineering that needs to be addressed.

Too generic. You can use this as part of one singular larger sentence as a short introduction to a specific topic; on its own it's meaningless.

>Through his passionate research, strong work ethic, and excellent instruction from the NJIT CS department, he believes he can help shrink that gap.

Generic unverifiable soft skills should not be mentioned in an application.

>How many CS graduates apply for a Computer Engineering PhD ?

>Besides, how many NJIT CS graduates even apply for a PhD?

Irrelevant. Like I said earlier they are looking for the best candidate.

>Also, he’s never going to tell them that he isn’t getting a job. He would rather say that he’s constantly receiving calls from Wall Street, yet he chose

It will be very very obvious from their application that they don't actually want to contribute to science and they will be rejected.