As a long time guitar player, I'm a bit confused, it seems on ukulele, it's quite common to use inverted chords (i.e. the root note is not necessarily the lowest note, in term of pitch) in substitute of those in root position (in order to simplify fretting I think). Is it true and widely acceptable?
Simply put, it has to do with how ukulele is played in common practice. It's similar to guitar in that you strum chords both up and down in rapid succession, the difference being someone had the bright idea to put a higher string as the 4th string, making it sound as if all the chords were up strums. This hides which strums are up and down and overall gives a brighter and more regular sound to it. Since chords aren't always constructed with the root on the top as well as the bottom of the chord, and a ukuleles small range and less strings, inversions start to sound very similar to root position chords. This is also helped by the fact that the ukulele is not often played as a solo instrument compared to being an accompaniment for singing or another ukulele. If you add a bass instrument the inversions don't really matter anymore.
From personal experience: it's very common on guitar as well, and ukulele is a more limited instrument, no reason to have to use all root position chords. Reasons:
Voice leading. Inversions can, in essence, allow playing two notes from two chords with a unison or semitone interval between them on the same string. Wow that was a bad explanation. Here you go.
Extended chords. No, this doesn't apply that much to ukulele. But 7/9/11/13 chords are often hard to play on guitar, unless you allow for inversions, which make some of them trivial. In fact, in the larger extended chords, it is common to omit the fifth, and if necessary, omit the root (with the assumption another instrument will be playing it). And on (a 4-string) ukulele, it is impossible to play a complete 5+ tone chord.
Inversions can help you move your hand less. If you are limiting yourself to root inversion only, you will find yourself going all up and down the neck.
Just a little addition to Ye Dawg's answer: I think that the obvious reason is that guitar has 2 strings more. (Note: I'm a classical guitarist, but I've never played ukulele, so take it with a grain of salt.)
Let's have a look at triads (minor/major chords (mostly)). If you play them on the guitar, you will find that you play all three tones on the higher strings in any inversion. But, fingering these three strings, you still have three strings left. That gives you a possibility to add any root whatsoever (try playing a chromatic scale from the lowest E to the next higher E — the farthest you need to go is the 4th fret) and possibly more.
On the contrary, after fingering these three strings, you have only one string left. So there's not a real choice, most likely there will be only one of the tones of the triad within reach, and so you just finger that one. Moreover, if you strum the guitar, you can choose where to start strumming and not strum some of the lower strings. Since on the ukulele, as far as I know, the lowest string is actually not the 4th, but the 3rd, you have to finger it somehow in order to be able to strum the other three without some weirdnesses like muting the string with your left hand.
And if this applies even to triads, then the more complicated chords, like 7ths, will make even more problems, and it looks like you should rejoice when you manage to finger them at least somehow :—).
True, on guitar, most chords - particularly the basic ones - seem to be shown and taught as root position chords. Often eventually played as all sorts of inversions, but root basically. The reason is that the most common triads can be played in E and A shapes, which often come together in pieces played, and use 6th and 5th strings as the root notes, respectively. That leaves 5 or 4 other strings available for other notes, some of which will be octave copies of those already played.
With 4 instead of 6 the uke is somewhat restricted in that field. Playing a shape which puts root on the bottom string leaves 3 others, pretty good. But playing a different shape around the same fret place will leave only a couple of other strings. Notes missing could be found on the bottom string, which then means an inversion is being played. So, it's more convenient for the player to stay around the same few frets and use inversions than to chase up and down the neck - which doesn't sound as good anyway.
I think the dominant reason is simply that ukulele is higher-pitched. In its register, you scarcely perceive any note as a “bass note”, hence there's also not really a strong effect of “inversion”.
Indeed, when you're playing with a guitarist or even bassist, what the uke does is completely irrelevant for the question of inversion, because it's always the bass instrument that defines this. Even when no bass notes are actually played, listeners may “mentally add” them.
All of this also holds true for other high-pitched plucked string instruments, like mandolin and balalaika.
The strings of a ukulele are tuned like the top four strings of a guitar with a capo on the eighth fret, and with the fourth string tuned up an octave. Most guitar chords are formed by producing either a rooted or inverted form of the chord on the top four strings, as convenient, and if the chord isn't rooted adding a root on either the fifth or sixth string. Ukulele chords are similar except that if the fifth or sixth string would be needed to play the root, it's omitted instead.
If one had a guitar but couldn't play anything on the bottom two strings, one could use a couple of movable chord shapes to play everything in rooted position, but having all notes of the chord move up and down parallel to the root would generally not sound very good. If one plays chords in the sequence C-G-D on the top four strings of a guitar, the C would be voiced c'-E'-G'-c'', and the D chord as d-a-d'-f#'; the G chord could be played as g-b-d'-g' or as g-d'-g'-b', but one of those would have to be a transposition of the preceding or following chord.
Further, while guitars may sound fine when played on the tenth or eleventh fret, the smaller size of a soprano ukulele would cause it not to sound good when played in such fashion. If one needed to play a rooted B chord on a ukukele, the "root" would be pitched higher than almost any melody performed by a non-amplified male vocalist, and many melodies sung by female vocalists, making it unlikely to function as a root.