Maybe not a final answer, I won't add references, as you may find enough in my relevant posts
Taqlid isn't per se something haram, as we are always asked to ask people who have more knowledge than we have by qur'an.
Ijtihad is something which is strongly recommended (if not ordered) all the time and no scholar would deny this and all would consider it as needed all the time.
There's no clear date when or even if "the doors of Ijtihad have been closed" as it is often stated. This is because we still have ijtihad on a lower level than what is called ijtihad al-mutlaq, an ijtihad which has it's own sources and basic elements such as qur'an, sunnah, ijma'a. qiyas, masalih, ... (osol al-fiqh) and not based on a predefined view.
But for example if you read the book or biography of the maliki scholars of qadi 'Iyad called tartib al-madarik ترتيب المدارك وتنوير المسالك لمعرفة أعلام مذهب مالك you may read in the introduction his statement saying that no where in al-Anadlus or al-Maghrib (meaning Spain. Morocco, parts of Algeria, Tunisia, Mauritania etc.) you may have the possibility to learn fiqh based on any other school than the maliki school.
Often the closure of the doors (or gate) of Ijtihad is connected to ibn as-Salah the shafi'i scholar... maybe he has written or said something like now there are only 4 madhabs (which until today isn't really true, as the dhahiri school has never totally disappeared).
So back to your question I'd say yes you are correct, after the formation of some madhabs during the 2nd and 3rd century after Hijra many students and scholars concentrated more on establishing and approving these madhabs, than on doing ijtihad (al-mutlaq), so these madhabs have been formatted established and well docummented, those madhabs whom had the less followers or lets say the lazier followers have disappeared due to the lack of documentation (it is funny that of all things a sufi like ibn 'Arabi was the transmitter -to the middle east- of the dhahiri madhabs books of ibn Hazm now most likely used by salafis).
But on the other hand if you asked scholars of the established schools or scholars in general about this they won't accept the statement, as there's still ijtihad on new events and issues and ijtihad inside of each school present even nowadays. Note that none of the 4 madhabs have kept all the views of the founders, but they have developed with time based on the founders osol...however this won't apply for for example the practice of people of Medina in the maliki madhab, as the situation has changed with time after Malik's death.
Also note that even if there might be a main view of each madhab on a matter there are other opinions inside a madhab, which shows that a pure taqlid isn't or wasen't present, but there were long time periods where there were not much scholars whom tried to actively do ijtihad especially after the 6th century after hijrah and there was even in some countries a more than intellectual dispute between madhabs because of taqlid, some say it started with the malikis in Egypt whom attacked imam a-Shafi'i --physically- however those were neither students of Malik himself nor scholars who are considered as "co-founders" or "of influence" in the madhab. Alao in some countries hanafis refused to marry shafi'is due to the fact that they can say:"I'm a believer insha' Allah" which was qualified as a doubt of Iman ...
One must also say that the benefit of having well defined madhabs is that we may have a clear interpretation of shari'a at courts, because there where a qadi can do his own ijtihad you may expect about anything which is possible according different views and interpretations of shari'a sources.
Is it necessary to follow a particular madhab?
What is the origin of the concept of four ways to follow Islam?
Can a person take individual opinions from any of the four schools or is it mandatory to follow only one throughout your life?
Is Taqleed Fard in Islam?
Why should we do Taqlid (follow a Mujtahid) in religious problems?
Origins of Taqlid
Is ijtihad open in Islam (Sunni view)?