In any case, you're not the only one to send paperwork by standard mail. Some people use registered mail and it's cheap for the peace of mind if they're the type to worry. I think it doesn't make any real difference. If the application gets lost, we have to send replacements, no matter if it's DPS or USPS who lost the paperwork.
When friends or coworkers apply, I tell them don't check the website for a month. There may be an update sooner. If they're really lucky they might get their plastic before then. But for most people it just seems to cause stress. And checking the website doesn't make it faster.
Check after a month. Three weeks if you're impatient. Once you see they have all the paperwork, find something to pass the time and be pleasantly surprised when the card shows up in your mailbox.
I know. Easier said than done.