If you're not doing your authorization properly, then no, basic ID obfuscation is not an extra layer of security. If anything, the fact that some people might gloss over the glaring security issues because "well its random ids so I never decided to check" is worse, an incremental id can at least be easily tested while developing to make sure, or a nice white hat hacker might notice and let you know.

Depending, very much, on that balance between usability and security. For the use case in the story, I'd way rather talk about (and write down) incidents 122 through 124 with my team, rather than incidents 549697a9-dd6a-4a90-a5f4-b2ff1a1d9289, d6150929-a692-414b-ba9e-ccbcf5e48a59, and 2756998d-035f-42bc-a97d-4135529e85d9.