I've tried all-fourths tuning quite a bit. To me, it definitely makes purely monophonic playing a lot more instinctive (even having got used to standard tuning) - any little one-octave scale shape you learn can be moved anywhere on the neck.
… but many things relating to chords become more difficult. In standard tuning, The D, G, and B strings make a lot of major and minor triads easy - barred, they constitute a major chord by themselves:
and from that, a two-finger hammer-on can be used to get to a chord a fourth up (as per the standard C-shape), which is a motion found in many rock riffs:
there's a minor shape playable that spans only one fret (as in the standard A minor shape), that would span two frets in an all-fourths tuning:
There's also a major shape that spans two frets (as found in the standard E major shape) that would span three frets in an all-fourths tuning:
...as would the similar minor shape:
Another thing that makes barre chords a lot easier in standard tuning is that with a full barre, the E, B, and top E strings constitute root and fifth (of an F-shape barre).
In rock soloing, the way that this minor third played on the G and B strings can be easily be bent to a major third by bending the B string is one of the archetypal sounds of bluesy playing - and that would be harder in all-fourths.
Subjectively, when 'mucking around' in all fourths tuning, I'd also say I came across many fewer 'happy accidents' in terms of stumbling across interesting-sounding chord shapes and riffs. Standard tuning may seem illogical, but a lot of good stuff seems to 'fall out'!
As a consequence a second advantage is that chords can more easily be translated to other fretted instruments tuned in fourths (tenor banjo, mandolin, ukulele, etc.)
It would do if they were tuned in fourths, but often they're not - mandolins are normally fifths (like violins), the ukulele typically has a re-entrant tuning with the same tuning kink as the guitar, and banjos often use open tunings. All-fourths tuning does make the guitar more similar to bass tuning, though. (Note it may make more sense to tune bass - even 5-or-more string instruments - to all fourths if you are focusing on monophonic playing, which may be more common with bass).
You might find some other information at Why is the guitar tuned like it is?, although I don't think that's been asked or answered from quite the same perspective as this question.