Hey James:
Don't wish to alarm you, just the facts.
I just came back from CA. I was stuck in Bishkek for 9 days waiting for my visa (Canadian AND I had an LOI).
I met a German woman who was there for 14 days - she did NOT have an LOI - and regretted not having one.
Some people were only waiting four or five days. It was beyond frustrating.
The woman (I use the term lightly) who controls access to the consulate is hostile, aggressive, nasty and unhelpful. She has a reputation for a reason.
All I can say is this: Go to the consulate and look for the information sheet on the gate (English). Follow the directions exactly and have every document it states in your possession. Call the minute you can - there is a phone number on the instruction sheet and the nasty woman will book an appointment for you. If you are lucky, you will not be there during a time when they are closed for three days or more. Once you have the appointment, arrive an hour early and wait outside the gate. She will appear from the doorway and call out your name close to the appointment time. Do NOT miss your appointment. Wear warm clothes as you have to wait outside. I waited for three hours outside. On the day I was to get my VISA their printer broke. It took three (yes 3) days to fix the printer - nobody could get a VISA because of this. Incredible.
Other people were getting their appointment in two days, then two days processing. Me, not so lucky.
Uzbekistan is outstanding by the way - by far my favourite country in CA. Don't let the hostile, narrow minded goat who works at the embassy turn you off. The people are amongst the nicest on the planet.
So, even if you do not need an LOI, I would get one if I were you. It seems to really grease the process.
Good luck and enjoy UZ.