Completely wrong. We see heavy influence of Perso-Islamic architecture even in deep south which was ruled by independent kings for most of medieval period. Sultans of Vijayanagar and Nayakas of Madurai adopted Persianized architecture even when they were completely independent.
There is hardly a single major city of medieval India which was not influenced by Perso-Islamic architecture. Jaipur which you mentioned is full of structures inspired by Perso-Islamic architectural tradition:
The point was not that every area that was under Muslims only had Islamic architecture, the point was reason for adoption was heavy military dominance of muslims. Your point is that Islamic architecture was adopted because of superiority, but this is not the case we see in Rajasthan. Before Mughals, there is no impact and look at architecture of Mewar during Kumbha, if Indians adopted it due to superiority, likes of Kumbha would have done that but they did not. Same with Vijaynagar, even their aqueduct did not know arches( despite knowing Muslims for centuries).
Jaipur was independent but was vassal of Mughals, Sawai Jai Singh could read and write Persian, however, likes of Maldeo or Sanga did not take interest in Persian so claim that Jai Singh adopted Islamic architecture due to latter's superiority is nonsense, it was cultural imitation on part of some weak Hindu rulers nothing more.
Gajapati kings did not adopt Islamic architecture at all because they were confidant of their own power, once Orissa came under Muslims, we see many Islamic structures. As for Vijaynagar, please show me some great impact( not one two isolated buildings easily explained by Turk presence) of Islamic architecture on city itself.
As far as Jaipur was concerned my point was about planning of city, read more on it, in case you argue that it was due to Islamic traditions of city planning which would need us to show any such planned city of Muslims in India.