No one likes the idea of the English Parliament being forced by a few generations of non-Home Counties nobles and their hangers-on who manage to dominate the succession somehow making it customary for Parliament to be rotated around the whole country forever? And all the deep consequences and constraints that will put on the English system?
Because of the inconvenience of the deliberative/consultive body being variously located and moved around and generally distant from necessary administrative centers, that puts considerable strain on it and means that over time, powerful kings and their supporters are likely to either break the rule and make it stay put in or near London, or simply discard it and go straight for absolutism. In premising this happens and that Parliament still exists as a relevant thing, I have been supposing that it picks up adherents who won't tolerate either its abolition or its being in fixed location, the idea being that its function as a check on royal power as well as a mechanism for tying royal power to the ruled people (it works both ways after all) becomes associated with its mobility as an essential aspect of what makes it representative and therefore useful.
Surviving, Britain is different because of it, and insofar as the Westminster system is the model for most European and former colony state systems OTL, either in the ATL English influence in this is less, or the whole world's concept of how the democratic element works is radically different.
So for instance, it would have seemed natural to the Virginia colonists, assuming some such analog existed, that their colonial House of Burgesses would meet in various places in the colony, and a lot of history that relates to conflict between the Tidewater regional dominance and the disgruntled western settlers might have gone very differently; similarly in Massachusetts and other Congregationalist colonies--it would be assumed that English people naturally must have an assembly that visits every corner as soon as there is adequate development there to house it, and Boston is just the biggest city, but not the automatic seat of democratic governance. Similarly if some analog of the revolutionary USA came into being and developed a Constitution analogous to ours, the idea of a single national capital might apply only to the executive branch, and it too might be made as decentralized as possible consistent with reasonable efficiency, while Congress and the Senate (and the Supreme Court, why not) rotates all over the Union. Presumably each state would have to prepare a suitable meeting site as a condition of admission or promotion from being a mere territory, and be encouraged to host it in a different site the next time Congress comes to that state, if they have grown enough to warrant it anyway--New York City would house Congress just for one 2-year session, and next time it comes to New York state it would be in Buffalo or Utica or someplace else. Meanwhile with the national fixed capital being strictly a center of executive power, it too might be more easily movable--no huge investment in developing DC, the Administrative center might be moved steadily westward every 20 or 40 years or so. Perhaps it would be allowed to settle in some fixed location that otherwise commands no particular reason to be developed, to stress that the power of the Federal state depends on the will of the governed to support it--so, out in the middle of Kansas, for instance, or at Colorado Springs (defensible in the nuclear age, after all, buried under Cheyenne Mountain perhaps)--someplace central but otherwise not desirable.
Oh, it may be impossible, but I'm suggesting the only way to break the logic of political power being sited at centers of other forms of power is to make the damn thing move around. And that the obvious inconveniences of that might be offset by an appeal to democratic ideology and the self-interests of the majority of the nation who will not have the privilege of living in the Center.