Why can’t I open voicemail on my phone?

Voicemail requires operator support. In other words, it requires support from China Mobile or China Unicom. China Mobile's Global Communications can open a voice mailbox, and China Unicom's card can also be used to record the voice message and then send it out. As for the Shenzhouxing public card you mentioned, it seems that this service is not available. You can check with the local 10086.