Firstly, I referred to the period of Ivan IV because you didn't referred to any period while you said about Moscow's association with its own Duchy. That's why I guessed that you probably had told it in the context of Peter I's reign. And what I've wanted to say, after all, this reason of Moscow's importance you mentioned had been outdated by 17-18 century. There wasn't any demand for capital to be associated with very one Duchy these centuries, because of ravages of time (and reign of Ivan IV).Well to be fair the other countries in that situation don't typically create neutral cities. Russia and the US have(it's a US staple at every level, build a specific city for governing that is relatively small).
I'm saying that's why Moscow was the capital pre St Petersburg. Muscovy conquered Russia and Muscovy's capital remained until St Petersburg. If some other duchy had unified Russia Moscow would not have been the capital until Peter the Great decided to change it or again during the Soviet era until now. It'd be just another major city. That's what I meant by it being given it's importance by being the capital of Muscovy. Even if the people there or leaders didn't care about that, that's why it was capital, same with Paris or Berlin. Over generations it just became the capital. I was not referring to a "problem" tbh think you're referring to something else, I wasn't referring to any events from Ivan IV's time just why Moscow became capital. Russia is one of the only countries to create a "government city for government city" though. Almost all of the major cities of the old world besides St Petersburg were founded MUCH earlier because almost no one else did that. Italy moved towards an ancient already existing city and the Germans and French kept their non neutral capitals and they became neutral over the passage of time(Berlin much more recently than Paris obviously). Most countries just waited for that association to fade away and if it didn't oh well. Feel Europeans and Asians see their biggest cities as appropriate capitals because it puts on the most impressive show for diplomats and before that because government=King and government city was going to be fancy as a result.
St Petersburg differs from Washington though in that you guys were trying to build an opulent showpiece city, and were replacing the importance of Moscow(in ancient history a lot of examples of this, in modern history it's unique though). Also unique in that most replacement capitals were pretty close to the old ones, cause that was usually the desirable region. St Petersburg was very far from Moscow. Washington was just a neutral site and in the beginning Washington was basically hell on earth(people joke about "cleaning the swamp" well it was literally a swamp). All it's importance comes from history and tourists wanting to see that but it's like the 19th or 20th biggest city or something like that aside from political stuff there's very little to do there and the same is true of most American state capitals. St Petersburg was built as a new neutral capital but it fit the profile of an old one.
Secondly, I think you're missing second reason of building a whole new capital in Russia. Yes, you're partly right about "showpiece", but it wasn't the whole thing. As I've said before, St. Petersburg has been built as a center of new, European-like country, which Peter was going to create. Many of old aristocrats, center of whom were Moscow, were against his policy. To go forward according to his plans, Peter needed a new center for the brand-new aristocracy, on which support he supposed to base his ideas. Voilá, we have St. Petersburg.
Moreover, the reason of placing new capital far away from the old one is clear for me: Peter was in the process of getting Sweden defeated and wanted to show all Europe that he stands confidently on the coast of Baltic Sea.
Finally, it was a personality of Peter I. He was literally obsessed with the sea.