Shuting down a room with 4k+ users takes more than 2h

This issue has been migrated from [#7651](https://github.com/matrix-org/synapse/issues/7651).

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### Description

It is not actually an issue, more a painful behavior.

I tried to use the admin API to shut down a room with 4443 local members (no remote users) and 4450 state events. It worked but took 122 minutes!

Here is a screenshot showing the users joining the new roow, it is quite slow:

The leave rate from the previous room was similar.

I do not claim to understand exactly what happens, but this seems very long to me, in particular when we know that the API call is synchronous. I think this API should be asynchronous, like the purge history API is.

It should be noted that purging this room was surprisingly fast: it tooks only 52s.

### Steps to reproduce

I don't think anyone actually want to reproduce it, but if you do here are the steps :p

1. create a new room
2. create 4k users and make them join the room (you probably want to script that part)
3. save the room's ip
4. `curl -X POST https://`

### Version information

- **Homeserver**: cloud.cervoi.se

If not matrix.org:

- **Version**: 1.14.0

- **Install method**: apt

- **Platform**: Debian 10, PostgreSQL 11, Python 3.7.3