As someone who's actually currently leveling all classes simultaneously on a new character, I dislike BLM but in no way is it the slowest to level.
Does it feel sluggish? Sure. It's still quicker at killing things than plenty of others, and if you're saying TTK isn't important for leveling time, I dunno what you're talking about. Dungeons? Faster TTK means faster dungeon runs. Questing? Same thing, clear objectives quicker.
Running a timer and comparing doesn't work unless you have a very big pool of data because there are a ton of other variables that impact it, such as what kind of groups you're getting in dungeons. You could have the quickest class in the game, but if you're with a bad group in a dungeon, that's going to negatively impact your leveling time more than any class differences.
It also completely depends on what kind of content you're doing in the first place. If you're spamming dungeons then yes tanks and healers will level faster than a BLM, but that's because of queue times, which are the same for any DPS class. If you're doing PotD or solo content, BLM absolutely beats healer classes at the very least (and most likely others too), because healer TTK is abysmal and TTK is the most important thing if you're blowing through PotD floors or quest objectives.