Does the UK wizarding population only being 3,000 sound right or should it be more?

So according to JK Rowling, the wizarding population in the UK in the 1990s would have only been around 3,000 people.

Yet, when you look at the number of students at Hogwarts, the fact that there's an entire shopping district (Diagon Alley) catering to the needs of the wizarding community, the fact they have a bank, their own currency, their own radio station, a wizarding only town (Hogsmeade), many other wizards living alongside muggles in the muggle world and the fact that there' an entire governing body (the Ministry of Magic) that exists just to govern over the British wizarding community, I feel as though the British wizarding community should realistically be at least around 15,000 to 30,000 as opposed to just 3,000.

However, I'm wanting to know your opinions. Does 3,000 sound right or should it be more?