On guitar, for most of my life, unless I was playing with others, when tuning I'd use the 5th-7th fret harmonics and listen to the 'beats' and then confirm with the fully-fretted 5th fret string-to-string tuning...
However, on most ukes I've played getting these harmonics can be an issue, which seems mostly to be due to the shorter scale length somehow, and for me, once I've confirmed/fixed the setup so that the instrument intonates well enough, I find that tuning with the open strings to a tuner is faster and more accurate than the 5th fret FOR ME.
If your instrument has issues with open strings vs 5th fret vs 12th fret being in tune, I suggest that your intonation is off, but most folks lack the hearing perception or the desire to develop more accurate hearing perception and will tune in the simplest way.
Also, lots of folks here on UU are 50+ yrs old, and hearing loss increases with age, as well as pride interfering with folks admitting the hearing loss and getting help (hearing aids) - which I've encountered often enough with others in my own life to realize that some folks are obstinate and just going to argue that they do not have hearing deficits, so I keep to myself when that happens.
Being 48 now, my hearing perception is better than ever, however if there is a 'white noise'. 'pink noise' or 'brown noise' present at sufficient volume it tends to mask my ability to perceive intelligible speech, but there are lots of times this is actually desired and often the reason for those 'sleep machines' that play digitized sounds of ocean waves or a torrential rain storm, as these also have a similar masking effect for most people.
So for the best way to tune your own instruments, do whatever works for you, as it is all based upon your own hearing perception.
The
'Holy Tuner-Use Magisterium' can be fully ignored if you wish.
However if you are in a group, and playing with others you
all need to be tuned to a
common pitch reference, be it A-440hz or just someone else's arbitrary pitch reference. For as they say, everything is RELATIVE.