There is at least one huge implication in 1 Corinthians 1:21. You're reading from the historical point, and I think that is right, but what you miss here is the fact that Paul was a jewish jew by origin, and that means that he held a specific notion of wisdom, which goes back in time for centuries (I personally think that it goes long before so called hellenistic culture, but some will argue on that for sure).
Philippians 3:2-7, ESV:
- Look out for the dogs, look out for the evildoers, look out for those who mutilate the flesh.
- For we are the circumcision, who worship God in spirit and glory in Christ Jesus and put no confidence in the flesh —
- though I myself have reason for confidence in the flesh also. If anyone else thinks he has reason for confidence in the flesh, I have more:
- circumcised on the eighth day, of the people of Israel, of the tribe of Benjamin, a Hebrew of Hebrews; as to the law, a Pharisee;
- as to zeal, a persecutor of the church; as to righteousness under the law, blameless.
So, I hope his origin is clear from these verses, and I can skip explanation of it. The point we need to extract from his words is the implication that Paul knew Old Testament very well.
And OT has its own flavour of wisdom definition, occasionally. Here is an illustrative part:
Proverbs 4:4-15, ESV:
- he taught me and said to me, "Let your heart hold fast my words; keep my commandments, and live.
- Get wisdom; get insight; do not forget, and do not turn away from the words of my mouth.
- Do not forsake her, and she will keep you; love her, and she will guard you.
- The beginning of wisdom is this: Get wisdom, and whatever you get, get insight.
- Prize her highly, and she will exalt you; she will honor you if you embrace her.
- She will place on your head a graceful garland; she will bestow on you a beautiful crown."
- Hear, my son, and accept my words, that the years of your life may be many.
- I have taught you the way of wisdom; I have led you in the paths of uprightness.
- When you walk, your step will not be hampered, and if you run, you will not stumble.
- Keep hold of instruction; do not let go; guard her, for she is your life.
- Do not enter the path of the wicked, and do not walk in the way of the evil.
- Avoid it; do not go on it; turn away from it and pass on.
Seems great, ain't it? What in the world can be wrong with these good words? Let's see what Paul himself says after he became an Apostle; and remember, before that he was a Pharisee.
2 Corinthians 11:23-30 , ESV:
- Are they servants of Christ? I am a better one--I am talking like a madman--with far greater labours, far more imprisonments, with countless beatings, and often near death.
- Five times I received at the hands of the Jews the forty lashes less one.
- Three times I was beaten with rods. Once I was stoned. Three times I was shipwrecked; a night and a day I was adrift at sea;
- on frequent journeys, in danger from rivers, danger from robbers, danger from my own people, danger from Gentiles, danger in the city, danger in the wilderness, danger at sea, danger from false brothers;
- in toil and hardship, through many a sleepless night, in hunger and thirst, often without food, in cold and exposure.
- And, apart from other things, there is the daily pressure on me of my anxiety for all the churches.
- Who is weak, and I am not weak? Who is made to fall, and I am not indignant?
- If I must boast, I will boast of the things that show my weakness.
I, again, don't know, if any explanations are needed here, because for me it seems clearly that he, being Apostle, actually came to state the opposite definition of Pharisee's wisdom, that we can read in Proverbs.
And now we can get a little bit back, to get sure that we are not messing things up. So, that is what Paul says after his confession of being a jewish Pharisee:
Philippians 3:7, ESV:
- But whatever gain I had, I counted as loss for the sake of Christ.
Therefore, my answer is yes, but not only that is misguided.
Now, specifically taking your considerations, I will even say that Paul actually trying to communicate a thought that there is no actual distinction between your first notion of "wisdom", second notion of it as "philosophy", and third definition of it as a "clear systematic modern thinking". Because all these things fall under so called natural wisdom, just with different faces.
As Mark Vestal precisely said in his comment, it is confirmed right in the next chapter, so here is related verses.
1 Corinthians 2:14-16, ESV:
- The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned.
- The spiritual person judges all things, but is himself to be judged by no one.
- "For who has understood the mind of the Lord so as to instruct him?" But we have the mind of Christ.
To answer your sub-question "what is permissible in the present age", let me just rephrase what he said — all things that falls under the mind of Christ are permissible, and whatever name you call a thing - is wrong, if it's not with the mind of Jesus, who made Himself known to us by doings, part of which are His words.
Hope that helps.