I'm not so sure we should think of Orthodoxy as an "offshoot." In the Middle Ages, the idea of a religious schism was a single entity that splits with both parts seeing themselves as the main body, not one sect that breaks away from a main body. And while Western and Eastern Christianity had very many theological differences, they spent the later Middle Ages off and on trying to reconcile--it's not quite a matter of heresy.

But more to the point here.

The thing to understand is that the Protestant Reformation was a failure. The story of western medieval Christianity is a story of waves of reformation--Carolingian liturgical reforms, Cluniac reform, Gregorian Reforms, the "reformation of the twelfth-century," the reforms of the thirteenth century that don't have a cute name, Observant reform...These were all ways of fixing one or another perceived wrong.

Martin Luther set out to do the same thing: fix what he perceived to be the flawed state of the c.1500 Church. Many of his criticisms weren't even original to him!

But earlier reforms and reformers had made their points and successfully redirected the Church, or at least redirected one part of it (various monastic reforms that swept through part of an order, or you could think of the Hussites as a reform movement), Luther and his companions...did not succeed. The Church based in Rome, which acknowledged its need to reform at the time, said flat-out "No" to Luther's version.

The change from reform to schism/Reformation involved above all the scope of the reforms, which was a direction function of the fact that the 15th century western Church actually increased lay access and participation! And yes, in response to lay interest. There's a really big rise in lay political and religious involvement from the late 14th century onwards.

This is my Actual Focus and I could go on forever, so let's not. But suffice to say that by 1500, average lay people were reading or hearing the Bible in their vernacular, including directly from priests in sermons; dioceses were offering the Eucharist to the laity multiple times per year instead of just the required Easter; &c &c.

So while earlier waves of reform involved the clergy, or monasteries, or a couple of monastic orders--this one involved a whole Church's worth of clergy AND laity who were often very, very invested in their religion. This meant on-the-ground worship. It also, crucially, applied to secular princes. In Germany, at least, they had spent the 15th century shaping up monasteries and even dioceses in their territories when the abbots and bishops wouldn't do it.

(The Church based in Rome, now the Catholic Church, went on to have its own major reformations later in the sixteenth century that you might see called the Catholic Reformation or Counter-Reformation).

Eastern Orthodoxy, of course, has its national/linguistic divisions that do carry liturgical and other differences--Greek Orthodox, Serbian Orthodox, &c. But there isn't a major schism there like the Catholic-Protestant break, true...but it is NOT for want of cataclysm.

Orthodoxy absolutely went through its own violent drama--multiple dramas, in fact. Just, these burned through the whole Church as one rather than fragmenting it. I am talking, of course, about iconoclasm.

And not the wimpy iconoclasm associated with the Protestant Reformation. Icons have a deeper meaning and significance in Orthodoxy than in even medieval western Christianity, in terms of serving as a conduit to God. Just, when the Eastern Church went through its waves of iconoclasm, reversal, iconoclasm, reversal, it did so more or less from the top down. And in the end, the theological situation wound up more or less back where it started--another reason for a lack of ultimate break.

So anyway, I think that asking "why the Eastern Church didn't have a Reformation" is less the question than "why did the Western Church have one." I know we live in an era of eight hundred thousand different churches, all claiming they're right, and so splintering ecclesiastical bodies is our default way of picturing things. But that absolutely wasn't the case by the Middle Ages. Including when Luther mailed his theses to the archbishops and said, "Hey, maybe you want to consider these points."