Actually, it's clearly in the grammar, so it's quite bizarre to have an aged novice constantly going against what the Word actually says and follow it up with claims he's proven something. Such is eisegetics.
You asked for purpose and
@GWH gave you one well-known verse with an actual statement of purpose in it tied to an explanatory verse with 2 more purpose clauses clarifying the main purpose.
I don't know if the response could have been any more succinct. But for the divisive eisegete, there's always another erroneous argument to be manufactured.
What is "clearly in the grammar"? This is just another fantasy of yours! You want something that is "clearly in the grammar", such as the truth, then consider this text:
Num 23:8-9
8 "How shall I curse whom God has not cursed?
And how shall I denounce whom the LORD has not denounced?
9 For from the top of the rocks I see him,
And from the hills I behold him;
There! A people [Israel] dwelling alone,
Not reckoning itself among the nations.
NKJV
The the term "kosmos" in Jn 3:16 can only rightfully understood to mean
all mankind w/o distinction! And this comports and harmonizes very well with other things John wrote such as:
Rev 5:9-10
9 And they sang a new song:
"You are worthy to take the scroll
and to open its seals,
because you were slain,
and with your blood you purchased men for God
from every tribe and language and people and nation.
10 You have made them to be a kingdom and priests to serve our God,
and they will reign on the earth."
NIV
Do you see what the text DOESN'T say!?
It does not say that Christ purchased every man [w/o exception] from every tribe and language and people and nation. Rather, it says that
Christ purchased men w/o distinction for God!
And,
Rev 7:9
9 After this I looked and there before me was a great multitude that no one could count, from every nation, tribe, people and language,
standing before the throne and in front of the Lamb. They were wearing white robes and were holding palm branches in their hands.
NIV
Moreover, a limited interpretation of universal sounding terms such as "kosmos" squares very well with God's specific promise in the Abrahamic Covenant that stipulates that God would make Abraham a father of many [Gentile] nations and that all nations (not each and every individual) would be blessed through him. God never made a universal redemptive covenant with the entire world in the distributive sense! But that redemptive covenant was made with all men w/o distinction in all the nations.
You clearly are reading into Jn 3:16 all men w/o exception -- conveniently forgetting that there can be NO EXCEPTIONS whatsoever if your universal, quantitatively unlimited interpretation is correct! Yet, again, in 1Jn 2:2, which I have exegeted often in the past, John himself EXCLUDES Israel from "the whole world"! Therefore, John's original audience (primarily messianic Jews) were made an exception by John! The "but" in the passage clearly makes a distinction between John, his original audience and the [Gentile] "whole world".
And Jesus himself was onboard with this Jewish understanding of the relationship between Israel and the Gentile nations. After all, he didn't pray for each and every person in the world in his high priestly prayer in John 17. He explicitly omitted the "kosmos"!
He prayed only for Abraham's spiritual descendants with whom God decreed to be in covenant relationship, i.e. the two flocks of His sheep who would become one.
Your man-centered, man-glorifying, man-exalting, man-praising abominable FWT theology is nowhere to be found in scripture -- least of all in Jn 3:16!