As far as I know, as long as there is exchange POP (Point of Presence) in the city (Refer to circular - NSE/MSD/45153 and Notice No. 20210331-61), there shouldn’t be much of a latency issue.
That said, the likely reason why the servers are located in Mumbai is because Refinitiv’s (formerly Thomson Reuters) Risk Management Layer and OMS (Order Management System) layer is also located in Mumbai (in the same Net Magic data center, mentioned in this support page).
From what I understand, due to the trading platform (aka Kite) and the Refinitiv’s OMS/RMS layer being within the same data center, they are likely in some kind of internal network, and latency between the two would probably be near negligible.
Hypothetically, if Zerodha’s server were located in some other city (like say Noida), then there would be an added time lag between sending orders collected from users via their servers to the RMS/OMS layer (This is based on the assumption that Refinitiv’s server is only located in Mumbai).
Also, as the exchanges are located in Mumbai, that would likely be the preferred location for having the broker’s servers. This is based on the assumption that there would be some kind of extra latency if the server location is further from the exchange. This last point is just my guess and maybe someone more knowledgeable would be able to clarify.
Also in case you are interested, you can refer to these threads - Room for improvement in zerodha tick speed and Concern about effect of Algo trading and Where are your servers located? Which region should i host my code for least latency? - Kite Connect developer forum