It has been 150 years since the independence of the Balkan countries. They had plenty of time to revive the national culture.
And still after all those years I can say that at least in Bulgaria (I have heard that it's the same and maybe to even greater extent in Serbia, Macedonia, Bosnia and other parts of the Western Balkans excluding Croatia and Slovenia who have been under Italian and Habsburg influence for much of their history) you can hear many words from Ottoman Turkish origin. There are many universal words which everyone on the Balkans can understand like Komshu, Byurek, Rakia, Kebap, Sarma, Tava, Yok, Cheshma, Megdan, Kalpak and many many more. Heck, even the word Balkan is from Ottoman origin you know.
There are many cities, villages, places in Bulgaria still holding their Turkish names even after the de-turkification that was undertaken in the country after it's independence in 1878 and during the Communist times. A big part of the cuisine on the Balkans and in Turkey is similar. Music and traditional dances also have a lot in common. Many Balkan people visit Turkey and vice versa too. In the past, especially during the Cold war it was hard to do it but now the borders are opened and people travel more and visit each other more often which I think is something good. I believe that The Balkan people have a lot in common. In that category I include the Turks from the Balkans and Western Turkey who are more linked to the Balkans in one way or another.
On the other hand there are still some big Muslim and Turkish communities on the Balkans outside of Turkish Thrace which by itself is home to 11 million people. In Bulgaria around 10% of the population is Turkish and probably around 13-15% is Muslim when you include the muslim Gypsies and the Pomaks that's between 700 000 and 1 000 000 people. You have around 200 000 Turks and Pomaks living in Northern Greece and around 6000 Turks living on the islands of Kos and Rhodes... I don't know the number of the Muslim Albanians, Arabs & Africans (mostly illegals) that are in the country though. Between 80 000 and 200 000 Turks are also living in Macedonia, a country where around 30 percent of the population is Muslim Albanian too and where compact numbers of Torbesh and Bosniak people live. Around 250 000 Muslim Albanians and Bosniaks are also living in Serbia currently. 20% are Muslims in Montenegro too- again Mostly Bosniaks and some Albanians. I am leaving Albania, Kosovo (where around Prizren there is around 50 000 Turks) and Bosnia aside which are all countries with Muslim majorities (and big/huge Christian minorities too) which are deeply connected to Turkey and the Turks in one way or another.
If I have to answer the question of the topic though it will be propably even longer than that post.
The short answer is "Money". The longer answer is much more complicated, especially when you consider that we are talking about a period of time of around 5 centuries. Period in which many things happened and changed. Just think about how much the world changed from the time your grandparents were your age.