But as far as I can remember, you can’t administer the rooms in a space as one. Like you need to be invited into each separate room.

Nope, again - I don’t understand who told you this. When you’re creating a room in Matrix you can make it either public, invite only, or only joinable via membership in a specific space.

Here’s a screenshot of the room security interface:

Image

Not saying that you couldn’t add that, I’m saying they don’t seem to want to “do what discord did”. Which is a bummer since the success of discord clearly shows what would be needed.

You are correct in that they “don’t want to do what discord this”: recently (and you can see this in their apps like EleX) they’ve transitioned to looking and acting more like modern mobile chat apps like Signal/WhatsApp/Telegram - a decision I’m assuming they’ve made as most of their funding comes from people who want a replacement for those apps and not Discord.

Regardless, just using a Discord-like client (e.g. Commet) is enough to get the experience you want.