Or for that matter, Long or Short Metre?
Many of the psalms in this collection are in one of these three metres. That is ‘the tradition’. It would have been nice to have produced a psalter with a wider range of tunes, as used by French, Dutch or Hungarian Protestants. There are some in this collection which use different metres. As it happens, though, for all their faults, the traditional metres do have their advantages. Hymnologists criticise them for this, but I believe the original writers in the C16 who put the psalms into metrical English were instinctively right when they chose the metres they did.
First there are a lot of available tunes in these metres. They were already standard for English songs. Singing the same psalm to a different tune can change its flavour and make it suitable for a quite different context. Common Metre is sometimes known as ballad metre because of the number of ballads written in it.
Second, it is difficult fitting verses from a language where lines appear to be irregular in length into a language where the musical convention is that lines and phrases should be consistent in length. Nevertheless, the average psalm groups its thoughts in lengths that often seem to be about right for the line lengths of the three conventional metres.
This cannot be a coincidence, since this turns out not always to be the case when one is trying to versify canticles which are taken from other parts of the Bible or from other sources.
Third, the metres are fairly flexible and not too difficult to write in. The French and Dutch tunes are not familiar to English speakers, and their metres do not necessarily fit English. The original is scripture. Fidelity to it means one should be cautious of inserting linguistic or poetical flourishes of ones own that are not in the text, or trimming sections that do not fit the metre. It would be much harder to make a psalm fit, say, a sonnet, without either having to omit elements or pad it out. One already begins to meet this issue when one chooses to put a psalm into a double 8 line form rather than a simpler 4 line form.