Let's look at the map in 1913:
(click for large)
Detail view 1913:
Omniatlas: Europe 1913: Aftermath of the Balkan Wars
"Greece according to the Treaty of Sèvres", in Wikipedia: Partition of the Ottoman Empire
These tiny remnants of Rumelia on both maps are not overly meaningfully described as "Empire's Balkan holdings".
The Empire's Balkan holdings, or Rumelia, looked as recently as 1861 more like:
Or even in 1912:
So, after the Great War, Turkey only emerged from the ruins of the Ottoman Empire and just held the line at its western border? Compared to its former "Balkan holdings", this is a really tiny strip of land in the historic Marmara region.
During the Turkish War of Independence and especially the Greco-Turkish War (1919–1922) the chaotically mixed settlement patterns of Greeks, Turks, and 'others' made it not overly convenient to base any considerations for future borders on 'historic precedent', 'rights' or even 'majority populations'.
Contemplating something like "Istanbul and the Balkans should have been given to Greece" – for whatever historical reasons, going back to late antiquity even – would mean that any armchair diplomat proposing such would ignore the past 800 years of historical development and the then present situation on the ground. That is of course great for nationalist expansion and a terrible idea for peace.
To rephrase the initial question:
Q Was there a reason why Turkey retained the rest of the Balkan territories of the Ottoman Empire, instead of adding East-Thrace and Istanbul to Greece or another of the Balkan states?
Yes. The Paris Peace Conference had terrible ideas for the future borders of a post-Ottoman/Turkish state. That caused a war in which the participants wanted to decide the argument with force. Turkey emerged from that war less defeated compared to other prying eyes and was able to largely retain the borders in its West as agreed upon in the concluding Treaty of Lausanne.
The Greek front collapsed with the Turkish counter-attack in August 1922, and the war effectively ended with the recapture of Smyrna by the Turkish forces and the Great fire of Smyrna.
As a result, the Greek government accepted the demands of the Turkish national movement and returned to its pre-war borders, thus leaving East Thrace and Western Anatolia to Turkey.
The Allies abandoned the Treaty of Sèvres to negotiate a new treaty at Lausanne with the Turkish National Movement. The Treaty of Lausanne recognized the independence of the Republic of Turkey and its sovereignty over Asia Minor, Istanbul, and Eastern Thrace. Greek and Turkish governments agreed to engage in a population exchange.
WP: Greco-Turkish War (1919–1922)