Which funnily enough, has bridges to Signal, Whatsapp, Discord, Telegram and some more, meaning you wouldn't have to have as many other clients installed to chat with contacts on those platforms
I remember looking into that a while ago, but it's not like I can just instantly hook up my WhatsApp or Telegram account into that, right? I'd need a server to act as a bridge.
And I wouldn't be so keen on giving that kind of access to a random server.
Yes your Matrix homeserver does have to run the bridges.
So I agree with you - you have to somewhat trust the admins of your Homeserver, or host your own homeserver and bridges. But I understand that the latter is not for everyone.
Although official tg bridges are meh: they have trouble with sending/receiving pics and loose messages from time to time. Plus those work for chats only (AFAIK)