I encountered an issue where I can't access the asset bundle I purchased because itch.io has closed the creator's page.

Itch.io has not responded to any of the emails I've sent and hasn't provided any assistance regarding the asset I purchased after they closed the entire page.

Does itch.io charge a service fee or take a revenue share from creators? Why does itch.io have the right to close assets that users have purchased?

Itch can close a project if it breaks a rule or law, some creators sell assets without having the copyright, sometimes they are stolen assets, etc.
Normally when that happens, Itch tries to return the purchases, but this will surely depend on the time that has passed, if it was a bundle or not, etc.
But as you can understand, if that content is stolen, Itch cannot leave it in its store.

Itch does not charge a service fee, each developer can choose to share a percentage of the sale, but it is not mandatory, some developers set the value to 0% and Itch receives nothing.

Other developers do direct sales, so Itch is not even responsible for the sale, even if the game or asset is distributed through Itch.

Sometimes the administrator reads and answers the messages, try to put the confirmation number that you received from Itch when you contacted support, so, if the administrator sees your message, he could give you a more detailed answer.

How do you know that Itch closed that account without also knowing why Itch closed that account?

But no matter who closed the account, Itch or the developer, if you purchased something without downloading, you should ask for a refund.

Also, if the content was removed for legal reasons, you should be informed, because using it in your projects might put your projects at risk.

You should also be aware that response time of support can be several weeks.