It can certainly go further than OTL, but it runs contrary to the trends of the period that saw almost every place at least nominally trend towards centralisation
That depends on which time frame you're looking at. The 12th and 13th centuries, when the movement really spread (as compared to the 14th and 15th, when it entrenched itself in places like Switzerland but was indeed on the defense in most other places), were a time of fragmentation in many parts of Europe, and not just because of the communes. Within the HRE, the stem duchies splintered into even smaller units. Iberia increased its fragmentation, too (Portugal...), and while from the look of it - because we know the outcome - France appears to have been on the path towards centralisation since Philipp Augustus, you might as well see it on the verge of breaking apart (Angevin Empire vs. Capetians, the South consolidating its distinctly different identity). The Southern rim of the Mediterranean was fragmenting, too, just like the Muslim Iberian states, the Byzantines gradually fell apart, and so did the Seljuks... the Kievan Rus, if it had ever been a close confederacy, experienced full centrifugality, and that's before the Mongols crushed it.
The one big cultural model that we associate with the Middle Ages that communalism really went against was knighthood.
Princely / royal militaries were predominantly (increasingly heavily armored) knights on (increasingly heavily armored) horses, with some peasant infantry strewn in that would get slashed down first in any battle, just like on the chessboard - with a social structure of a warrior nobility doing mostly that, living off their delineated land's peasant workforce (when they didn't go plundering), and creating their own unique courtly "high culture" around this very time, too, when they didn't fight, with its own types of poetry, music, sports, code of conduct etc.
Communal militaries were predominantly professional infantry (even though they had horses, too) with unprofessional infantry added on top in times of dire need, and in those places where they were strongest (Northern Italy again), they came to follow their own type of commanders (condottieri). In towns, a different brand of culture developed, with its own narrative genres, festivities (carnival!), institutions etc.
So, one essential question here probably is how strong the military advantage of knightly cavalry was around that time, and what communal armies could effectively bring to bear against them beyond numbers before the advent of gunpowder...
(with Italy coalescing in regional states and other countries getting even wider unions)
One question I've been pondering is to what extent the perennial battles between Guelfs and Ghibellins, in which many Northern Italian cities converted from communes to military dictatorships to larger hereditary military dictatorships, are attributable to the inner dynamics of urban leagues like the Lombard League (speaking of the Greek leagues of poleis as an example) and to what extent they were externally induced by the rivalry between Holy Roman Emperors and the Papacy.
To put it differently: If Fred Barbarossa had died in a devastating defeat at Legnano, for example, would the Lombard League have consolidated into some type of Northern Italian "Alte Eidgenossenschaft", or would it have fallen apart into warring factions like it did IOTL?
and the bigger ones go on to dominate European politics and colonisaion of the whole Early Modern period.
Yeah, sure. That's what fascinating me so much about it. The possibility to imagine an entirely different starting part for the transition from Middle Ages to Early Modernity, and thus a different Modernity, too.
Which should not be mistaken for some kind of utopian thought experiment in wishful thinking. There's lots of genuinely ugly aspects to the communal model, too: While we can pinpoint the big systematic expulsions of Jews, for example, to emerging territorial monarchies, there were tons of "spontaneous" pogroms against the local Jewry happening in dozens of quasi-independent towns all over the place, too, to name just one example, and they were often more violent and gruesome than the forced relocations that are better known today.
I also think you're massively over-estimating the correlation of communalism with capitalism (and progress); it eventually emerged in places that hadn't had a serious communalist movevemt long since (Belgium and the Netherlands) or ever (England), while areas that persisted into communalism well into the 18th century eventually found themselves poorer and outdated like Genoa or Venice did - or eternal exporters of mercenaries like Switzerland.
Not necessarily progress, no. I can even well imagine Communalism-wank TLs in which there isn't really any sharply felt transition into Early Modernity around the 15th and 16th centuries at all.
But capitalism, yes. While it was massively helped by some centralised monarchies and their empires later on (and held back by others), it did develop in urban communes, and spread with the legal codes that were copied from one town onto others and the social structures they created. I would go so far as to say that if we went in the other extreme - screwing the communalist movement entirely and right from the start, having only strong monarcho-chivalric states controlling crafts, commerce, and legal courts everywhere throughout the Middle Ages, then it may well have been that capitalism as we know it would never have developed at all in Europe.
The examples you gave also make me wonder whether you differentiate between "capitalism" and "industrialisation". Between Florence and Antwerp - to just take two examples - genuinely capitalist inventions like financial markets were created centuries before industrialisation took off. Also, the Low Countries were both a hotbed of communalism in the Middle Ages AND one of the few urban-dominated confederal republics of Early Modernity, resulting from a war of independence of, basically, a league of cities with some backwater, against the biggest centralised-monarchical dynasty of Europe, so not really a good counter-example, even though it did consolidate into a centralised state. Its religious dimension had, again, I think, a lot to do with how the rift between aristocratic and urban cultures played out IOTL.
England was a relative late comer to the capitalist party, and then overtook everyone through its combination of the slave-based imperial trade triangle and carbo-industrialisation.
Europe probably is poorer and weaker overall due to it, quite possibly to a level that allows the Ottomans to get deeper.
That may be the case (and really depends on how we estimate the advantage of professional heavy cavalry).
Another interesting thing to explore: communalist structures evolving into modernity under the umbrella of a pax Ottomanica... The Ottomans were pretty adaptive in how they dealt with their Christian European subjects at first. Where the limits of that are is another thing I can't fathom yet.
But good food for thought - thank you for your reply!!