"Proof-texting" can be a way to bypass a thorough-going hermeneutic. I emphasize the words can be, because in Christians' witness to the world, there is nothing inherently wrong with quoting a verse "out of context" when the situation warrants it.
Verses like John 3:16, among others, is a great verse to quote to a seeker, and the Holy Spirit, I believe, is willing and able to implant the meaning of that verse into a seeker's heart. Sometimes that soil upon which that seed falls will be receptive to it, and the seed will germinate as the Holy Spirit wings the truth of that verse to a seeker's heart.
On the other hand, proof-texting carries with it the danger of eisegesis. To combat the tendency of interpreters of Scripture to project their own ideas onto (and into) a text, God has given them 66 books(!) from which they can, in analogical fashion, contextualize a pericope, making it clearer through what could be called a system of checks and balances.
That system of checks and balances can prevent, in many instances, an interpreter from over-emphasizing or under-emphasizing an aspect of biblical doctrine. Sometimes, however, the Bible presents us with paradox, and while some paradoxes can be reconciled, some cannot.
An example of paradox that can be reconciled quite easily is Jesus's teaching about gaining life only to lose it, and losing life to gain it (see Mark 8:34; Matthew 16:24ff; and Luke 9:23ff).
TOWARD MY BOTOM LINE
An example of a paradox that cannot be reconciled that easily--if at all--is the paradox of "the free will of humankind" and the "Sovereignty of God." According to Reformed Theology, the supposed paradox of which I speak is not a paradox at all. Rather, it is a clear-cut issue that when rightly understood takes "free will" out of the equation in order to give way to God's sovereignty. Free will to Reformed Christians is a spurious construct that robs God of his right to choose his elect and gives humans the freedom to believe or not believe for their salvation.
Free-willists, on the other hand (i.e., Arminians), while not detracting--they believe--from the doctrine of God's sovereignty, insist that humankind does have the ability to believe or not believe, else how can anyone make sense of the numerous invitations in Scripture to believe, to take that first step of faith (whether in a pinpoint of time or gradually over time). Crassly, you don't extend an invitation to someone you know in advance is not able to accept it. Jesus did not say "Come unto me, you elect ones." He said, "“Come to me, all of you who are tired and have heavy loads, and I will give you rest" (Matthew 11:28)
I'd like to think that both camps believe in the drawing power of God the Father and the Holy Spirit to regenerate sinners who are dead in sin, which brings me to my conclusion regarding your interpretation of John 6:64-65.
What the passage under consideration does quite nicely is simply corroborate other scriptures that teach the same or similar aspects of the same doctrine; more specifically, the doctrine concerning God's role in making corpses who are dead in sin come alive in Christ. If you want to "read into" John 6 the concept of total depravity, I do not think you are necessarily violating a hermeneutical principle, but I think you need to look elsewhere in Scripture for corroborating evidence ot total depravity. I assume there are plenty of evidences.
I think author A. W. Pink makes a valid point in his classic work, The Sovereignty of God and the Free Will of Man, in which he suggests there exists an antinomy between God's sovereignty, on the one hand, and man's will on the other hand. Think of an antinomy as the kind of paradox that is impossible to explain and reconcile. That suggests that both the free-willists and the election-emphasizers are only partially correct on this crucial and often schism-producing, two-perspective issue.
MY BOTTOM LINE
So why, I ask, is each side so adamant in insisting that only their perspective is correct? Why are proponents of each perspective so willing--even eager--to pick apart the perspective of the supposedly opposing camp (viz. Calvinists versus Arminianists) instead of letting the two perspectives remain an antinomy?
In conclusion, frankly I think the primary reason for this standoff is pride and the desire to be right at any cost, even it it leads to schism, bickering, disunity, grudges, bitterness, factionalism ("I am of Paul" and "I am of Apollos"), ad hominems (i.e., name-calling), and other God-dishonoring behaviors that potentially sully Christians' witness to the world.