I had applied for CVE ID at https://cveform.mitre.org/. I did followed their guidelines, and did exactly as their instructions said (didn't add PGP key as it seems optional). It's been 2 month since then and all I had received is confirmation letter that they had received my request and it will be reviewed . Then I made another request following their guidelines for issues, and again there is only confirmation letter (i checked spam). At their guidlines/FAQ they don't state how long review takes, what is possible estimate? What to do if I don't receive answer at all?
It seems for most cases cve assigned automatically in next 24 hours. When they have technical issues they post them at https://cve.mitre.org/news/. I had an issue due to badly configured filters in my email. I was able to receive letters from CVE-Request@mitre.org, but not from other *@mitre.org senders. Keep in mind that some mailboxes like gmail can block some emails entirely (so they don't even appear in spam folder).