I also think it's morally wrong as well. I can understand getting this request from someone who doesn't really know you and wouldn't know what to say, but getting this from someone you invested time with and has the capability to write you a sincere, positive LOR is inappropriate IMO. I understand people are busy, but given enough time, they should be able to handle it.
I spent over 500 hours volunteering at a local family-run office, any they asked me to write my own LOR. Frankly, I didn't feel right doing this and I was a little insulted that someone who knew me that well couldn't take 45 minutes out of their schedule in the course of three months to write me a LOR. I ended up not pursuing this option, which definitely hurt my app, but at least I know that I'm providing a 100% authentic picture of myself to the ADCOMS. I don't care if this system is a sh** storm for the most part - that doesn't mean I have to compromise my own morals.
When I become a physician and am on the receiving end of this, I'm going to be straightforward with people when they ask me for a LOR. If I haven't spent enough time with them to actually know them, I'll tell them that. If it's not going to be a great one, I'll also let them know. But if they're a genuine person and I want to see them in medical school in the future, you can be damn sure I'm going to carve time out of my day and write that letter with my own hands.