Interestingly, there does seem to be some logic and planning behind the distribution of the vowels. Whether the consonants also show any planning in their distribution is not quite so clear, though I think there are signs of intentional regularity and grouping of the consonants.
Firstly, the vowels occur at almost regular intervals:
A BCD E FGH I JKLMN O PQRST U XYZ
The regularity becomes more evident if we write the alphabet as the Romans wrote it. They had no J or K; they wrote V, not U; they had no W; and I think they had no X, Y or Z. Thus:
A BCD E FGH I LMN O PQRST V
They used V for a sound that was sometimes "oo" and sometimes "w", so to them V was a vowel. All the other vowels are separated by 3 consonants; maybe they put the vowel V at the end instead of after R so that the alphabet began and ended with a vowel?
Secondly, there seems to be some intentional logic in the order of those vowels (A E I O U), when pronounced as the Romans did, and as most European languages still pronounce them: it follows at least approximately a circuit around the mouth. The vowels are partly defined by where the forward hump of the tongue is. Roman A had the hump of the tongue drawn back and low down; Roman E had the hump forward and medium high; Roman I had the hump about as far forward and high as it could go; Roman O and V (the latter pronounced oo) had the hump further back, but I am a bit vague about how far back and how high or low.
Thirdly, I think there are some weak signs of planning in the order and grouping of the consonants.
BC (the C being pronounced /k/, not /s/ in Roman times) compares with FG: B is a bilabial plosive, F has at times been pronounced as bilabial approximant, meaning it has at least sometimes been pronounced by simply blowing through slightly parted lips. (In fact this is how Dr Johnson in his 1755 Dictionary of the English Language describes the pronunciation of F in the English of his day!!). C is a voiceless velar plosive, G (in the Roman /g/ pronunciation as in the English word "get") is a voiced velar plosive. How D might be compared to H I do not know. Then L, M and N are all voiced sounds that can be pronounced continuously with no sound change. (I do not know how a linguist would express that ...) Finally, P, Q, R, S and T may just be a collection of left-over consonants. The appearance of logic in the arrangement of the consonants seems decidedly less convincing to me than for the vowels, but that may be due to the difficulty of arranging consonants in any kind of order, especially before the days of X-rays, since no one could see inside anyone's mouth to be sure what was going on.