My problem with using the Image ID would be is it seems to be harder to implement appending additional Incremental/Differential images to it if the ID is a randomly generated string. But, you say this random renaming is only on Full backups? If so, I think I noticed this myself yesterday. Last year's Full backup was named a different string from yesterday's Full backup of the same partition.
EDIT: After reading your follow up post, I can see why Image ID might be preferable. It doesn't really apply to me. I, too, use dedicated, descriptive directories, so I could use either my descriptive user defined file names or an Image ID. And I don't get confused by multiple images because I generally run Full backups so the retention is only for 1 day, since the scheduled tasks only run at multiples of time of more than 24 hours. And I generally only use Incremental images, never Differential. And even when I do use Incremental backups, it's only within a 24 hour period between daily backups. They're used before I install/update software/Windows or make some kind change to Windows that I might need to roll back from.
Thus, due to the way I take backups, adding 1's, 2's, etc. to the end of my file names doesn't confuse me. In fact, I prefer it that way because I tell that X backup was Y backups after the morning backup. Plus, I generally go by the date/time stamp on the file. And, if I need absolute clarity, I load the chain of backups in Reflect and check the Comments I put on the backups. It also gives me an overview of the times when they were generated, too.
So, it's nice to know that there are choices depending on what you prefer.