Most of these questions ask for subjective answers, but in the spirit of this site I will try to answer from a hermeneutical perspective. :)
Is there anything inherently wrong with alcohol or getting drunk?
There is no prohibition in scripture to the drinking of alcohol, but drunkenness. This does suggest that the drinking of alcohol itself is not inherently sin, rather the abuse of alcohol is. Practically, alcohol does have positive benefits and was used remedially in the Hebrew and Hellenistic ages. In fact, in our modern age alcohol is still used remedially for various stomach and intestinal syndromes.
Despite alcohol having no prohibition in scripture, most scholars agree that expensive wine in both Hellenistic and Hebrew ages was non-alcoholic. For this reason, many theologians agree it was non-alcoholic wine that Jesus provided in miracle of turning water into wine. Notice Johns choice of words as he makes a distinction between the two wines, "Every man serves the good wine first, and when the guests are drunk, then he serves the poorer wine; but you have kept the good wine until now.” (John 2:10, NASB). This is perhaps the only distinction in scripture that alludes to the inherent state of alcohol as "poor" or ἐλάσσων wine. The Greek word ἐλάσσων only occurs 4 times in scripture so it is very difficult to gain a comprehensive understanding of the word. However, the LXX mostly used ἐλάσσων as a translation of "lesser." Clearly, there is an allusion here to Jesus' wine being superior in value to the "lesser" wine that is often provided at the end of parties. This can be interpreted as a clear distinction between "poor" alcoholic wine and "valuable" non-alcoholic wine. Ultimately, these are only allusions and do not provide sufficient evidence of the supposed inherent sinfulness of alcohol.
It is difficult to answer your question hermeneutically as right and wrong is largely subjective. However, I believe there is a good compromise found when comparing the change in soteriological focus between the old and new testament. The over arching soteriological theme in the old testament is over the question, what is sin? However, the major principle in the new testament is less about what sin is and more so, what is wise? This difference can be used in how we interpret what's right and wrong from a hermeneutical perspective. As a child, jumping over a fire can be thrilling and make for a fun time and the bible doesn't say that jumping over a fire is sin, but is it wise? In this case, what is sin is not the same as what is wrong. This is why the new testament focuses less on specific sin and more on sinful nature. After all, it is sinful nature that compels people to make wrong choices. In the case of the child, risking both future consequences and potential bodily harm for the sake of a thrilling experience is not a specific sin, but does reveal a destructive sinful nature. If this hermeneutical principle is applied to the case of alcohol, the drinking of alcohol in some cases, despite not being sin, can be hermeneutically interpreted as wrong in light of the potential risks.
Why will drunkards not inherit the kingdom of God?
Lets shift our focus to a hermeneutical approach: Why did Paul say what he said?
Our historical context involves Paul speaking to a church body who is struggling to find their identity in Christ as they wrestle with their past hellenistic ways. For drunkenness was merely one of the many struggles the people had as they journeyed into relationship with Christ: sexual immorality, idolatry, apostasy, stealing and greed were among others.
Our literary context involves Paul himself writing a letter to these struggling people. In our world, Paul would be considered an academic expert, he trained under the best Rabbis and acquired great skill in apology and philosophy. For this reason, we should be expecting an apologetic structure to his writings. Paul isn't going to just randomly throw out statements and hope for the best, no, Paul is going to think and intentionally structure his writings in a way to get his point across clearly and persuasively. Why is this important? Because we should be expecting a conclusion to Paul's assertion of drunkards and this conclusion can show us why drunkards will not inherit the kingdom of God. What we find in the following verses are two conclusions, one direct conclusion to the verse of the drunkards inheritance, another conclusion to the broader passage about the Corinthians sin.
(Direct) Such were some of you; but you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus Christ and in the Spirit of our God (1 Corinthians 6:11, NASB).
Paul's direct conclusion reveals his purpose to the mentioning of drunkards was to draw them to the hope of salvation. Thus, drunkenness inherently opposes this salvation. Notice how Paul divides the process of being washed into both sanctification and justification. Paul indicated that there were some people who were drunkards and had been washed...but you were transformed [sanctified], but you were declared righteousness [justified]. Clearly, labeled drunkards can receive salvation but only by way of being washed. Therefore, according to the direct conclusion drunkards do not inherit the kingdom of God not because they drink alcohol, but because they do not accept Christs provision of justification or his help in sanctification.
(Broad) Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God, and that you are not your own? For you have been bought for a price: therefore glorify God in your body (1 Corinthians 6:19-20, NASB). Notice the three themes to this verse, each theme reveals new insight to this topic.
The Holy Spirit is our Gift: "do you not know that your body is a temple of the Holy Spirit within you, whom you have from God..."
Do not quench the Spirit...hold firmly to that which is good, abstain from every form of evil (1 Thessalonians 5:19, 21-22). This verse indicates that sin (drunkenness) in our lives means we will miss out on a thriving Holy Spirit.
Life is a Gift: "and that you are not your own? For you have been bought for a price..."
Recognise these Gifts: "...therefore glorify God in your body."
Is there a commandment that explicitly prohibits drunkenness? Is it possible to get drunk in a "righteous way"?
Be of sober spirit, be on the alert. Your adversary, the devil, prowls around like a roaring lion, seeking someone to devour (1 Peter 5:8, NASB).
And do not get drunk with wine, in which there is debauchery, but be filled with the Spirit (Ephesians 5:18, NASB).
But be on your guard, so that your hearts will not be weighed down with dissipation and drunkenness and the worries of life, and that this day will not come on you suddenly, like a trap (Luke 21:24, NASB).
According to scripture, drunkenness is a "sinful way," opposite of a "righteous way."