"If you will let me be, I will try them."

(Grammar Questions I Couldn't Answer)

We've been reading a lot of Green Eggs and Ham to our daughter, and my wife (L1 Vietnamese) thinks she found a grammar mistake in the book.

" 'If you will let me be, I will try them.'  It should be 'If you let me be, I will try them', right?"

Indeed, this is what we teach when we teach English as a foreign language.  When teaching the first conditional for possible futures, we teach it as "if+ present simple, will + base form" e.g. "If it's nice tomorrow, I'll go to the beach." (See my worksheets on the first conditional, and on conditionals).
But I've read in some grammar books that the ESL textbooks are actually over-simplifying the conditionals, and in reality a lot of different structures are possible. So this was my first response to my wife.
...but then I thought about it a while longer, and I wondered if there might be a better reason why "will" was in the if-clause in this sentence.  Was it because this was not just a condition, but an offer?
I'm not 100% sure, so I thought I'd throw it out to the Internet to see if anyone else had opinions.