To the O/P. I think you answered you own question in the first line of your post when you say "considering I'm not incontinent". To try to get diapers given that fact would be nothing less than fraud!
You should be aware that insurance companies (or the failing health service this side of the pond) will only look to 'prescribe' and pay-for diapers if 1) you are incontinent and 2) other avenues have been explored. As you say, a doctor has to say you're incontinent AND that diapers are the best option. And no he's unlikely to take your word for it!
Most people do not like diapers (funnily enough) and therefore your urologist (who you will see numerous times) will try all sorts of things including drugs, exercises, diet changes, catheters and perhaps even surgery before giving up and saying have diapers. Also at each stage you could be subject to exams such as sleep clinics (for bed wetting), X-rays or even a camera inserted into various orifices! They may not question the fact that your incontinent but diapers are not something they will give straight away as they want to cure you!
Please be considerate to those who have a genuine need (older folks, people with spinal/bladder/bowel damage etc) - who's time with the specialist you would be using. Also the rest of us premium/tax payers who would foot the bill!
If diapers are important to you then consider budgeting for them like anyone else would for any other material item. If it means a few less beers after work or a few more hours in the office then so-be it but don't make us foot the bill for your urges! I know economic times are hard but at the end of the day you could consider investing in a set of washable diapers that would save you in the long-run.
For those of us with a paraphilic (NOT paedophilic!) obsession with disposable, it can only be more expensive 😢. Speaking of which I need a new case now, I'll have to find my credit card though....
Good luck, I hope we've all given you something to think about.