The misconception does not follow from the reasons given, and the reasons ignore a great deal of information.
As stated earlier, Islam is a complete way of life. Given this, it is not surprising that the Creator is concerned with the method which we choose to govern ourselves. The preeminent rule which the Islamic state must observe is stated in the Qur'an (translation follows):
[4:59] O you who believe! Obey Allah, and obey the Messenger, and those charged with authority among you. If you differ in anything among yourselves, refer it to Allah and His Messenger, if you do believe in Allah and the Last Day; That is best, and most suitable for final determination.
From this verse, it is clear that the state's obligation of obedience to the Creator is as important as the obedience of the individual. Hence, the Islamic state must derive its law from the Qur'an and Sunnah. This principle excludes certain choices from the Islamic state's options for political and economic systems, such as a pure democracy, unrestricted capitalism, communism, socialism, etc. For example, a pure democracy places the people above the Qur'an and Sunnah, and this is disobedience to the Creator. However, the best alternative to a pure democracy is a democracy that implements and enforces the Shari'ah (Islamic Law).
The Creator also states in the Qur'an (translated):
[42:36-38] So whatever thing you are given, that is only a provision of this world's life, and what is with Allah is better and more lasting for those who believe and rely on their Lord, and those who shun the great sins and indecencies, and whenever they are angry they forgive, and those who respond to their Lord and keep up prayer, and their rule is to take counsel among themselves, and who spend out of what We have given them.
Allah orders us in this verse to conduct our matters by taking counsel among ourselves, or by consulting each other. This is the methodology of the Islamic state, to consult one another, but to always keep the Qur'an and Sunnah paramount. Any law which contradicts the Qur'an or Sunnah is unlawful. This broad principle of consultation is certainly wide enough to encompass a form of government where all are heard - in fact, encouraged to be heard. The early Islamic states were of this form. The petty governments of many `Muslim countries' today do not apply this principle and in fact commit many crimes against the people.
As for slavery, Islam is unique among the `religions' in its close attention to the peaceful removal of this practice. Before the advent of Islam, slavery was widespread all over the world. The Messenger of Islam taught us that freeing slaves was a great deed in the sight of Allah. From the Sunnah, specifically in the study of the Sunnah called Sahih Bukhari, we find:
[3:46:693] Narrated Abu Huraira: The Prophet said, "Whoever frees a Muslim slave, Allah will save all the parts of his body from the (Hell) Fire as he has freed the body-parts of the slave." Said bin Marjana said that he narrated that Hadith to `Ali bin Al-Husain and he freed his slave for whom `Abdullah bin Ja'far had offered him ten thousand Dirhams or one-thousand Dinars.
Also from the Sunnah, specifically in the study of the Sunnah called Malik's Muwatta, we find:
[38:9:15] Narrated Aisha Ummul Mu'minin: The Messenger of Allah, may Allah bless him and grant him peace, was asked what was the most excellent kind of slave to free. The Messenger of Allah, may Allah bless him and grant him peace, answered, "The most expensive and the most valuable to his master."
The Creator has also made it easy for slaves to gain their freedom. From the Sunnah, specifically in the study of the Sunnah called Sahih Bukhari, we find:
[3:46:704] Narrated Abu Huraira: The Prophet said, "Whoever frees his portion of a common slave should free the slave completely by paying the rest of his price from his money if he has enough money; otherwise the price of the slave is to be estimated and the slave is to be helped to work without hardship till he pays the rest of his price."
The condition of slavery is very different in Islam than the harsh conditions imposed by non-Muslims or disobedient Muslims. From the Sunnah, specifically in the study of the Sunnah called Sunan Abu-Dawud, we find:
[41:4957] Narrated Abu Hurayrah: The Prophet (saw) said: None of you must say: "My slave" (abdi) and "My slave-woman" (amati), and a slave must not say: "My lord" (rabbi or rabbati). The master (of a slave) should say: "My young man" (fataya) and "My young woman" (fatati), and a slave should say "My master" (sayyidi) and "My mistress" (sayyidati), for you are all (Allah's) slave and the Lord is Allah, Most High.
Also from the Sunnah, specifically in the study of the Sunnah called Sahih Bukhari, we find:
[3:46:721] Narrated Al-Ma'rur bin Suwaid: I saw Abu Dhar Al-Ghifari wearing a cloak, and his slave, too, was wearing a cloak. We asked him about that (i.e. how both were wearing similar cloaks). He replied, "Once I abused a man and he complained of me to the Prophet. The Prophet asked me, `Did you abuse him by slighting his mother?' He added, `Your slaves are your brethren upon whom Allah has given you authority. So, if one has one's brethren under one's control, one should feed them with the like of what one eats and clothe them with the like of what one wears. You should not overburden them with what they cannot bear, and if you do so, help them (in their hard job)."
As a result of the teachings of Islam, slavery was almost completely eradicated from many areas of the Muslim world, peacefully and without bloodshed.