Looking at the current world records there doesn't seem to be a clear evidence that would indicate that bikes are considered better all around.
I assume that any trend you are noticing among your average Joe youtuber wanabe is the effect of an historical lingering memory: Bikes were far superior to Kart in Mario Kart Wii.
Back in Mario Kart Wii bikes had
- better speed thanks to wheelies providing a continuous bost
- better drifting on average (most bikes had inside-drifting and that was generally preferred)
- better handling
- worse mini-turbo (they could only access the level one "blue" version) but that wasn't significant enough to be an issue
Wheelies were supposed to be balanced by an increased weakness to "damage" - even just bumping into another car would drop your speed significantly. But that didn't really work out since when the rubber band AI wants you dead, it doesn't really matter if you are playing as the lightest character driving a feather or as Metal Bowser driving a war tank...
Furthermore, there is no one that can hit you during time trial.
Fast forward to Mario Kart 8 and Nintendo removing wheelies. Now bikes are far more balanced but apparently some players still favor them. I can see two main reasons:
- they genuinely prefer how bikes handle compared to kart
- they are victim of an afterimage memory that "bikes are OP" even if that is no longer true.
It is also worth noticing that even in Mario Kart Wii any bike had a similar stat kart counterpart so the difference was basically due to handling (bikes had sharper turning, inside drifting was preferred etc) and the wheelie gimmick. Now that the handling has been somehow nerfed and the wheelie removed I don't think that there is still any reason to always favor bikes to karts.