Your assumption is correct. Natural languages are extremely redundant and compressible in sound as well as in orthography, and this has significant and obvious benefits: you can understand obscured speech, read obscured text, and, yes, get the sense of a word based on a quick visual hook rather than relying on a purely phonetic transcription.
English orthography reflects its countless generations of development. The spelling of a word may not correspond perfectly to its pronunciation, but to select a spelling that does correspond to a specific pronunciation naturally excludes some others. I've heard native speakers, for instance, who have different pronunciations for all of "to", "too", and "two".
Further, since the orthography often reflects the etymology, you can often make an educated guess about the meaning of a word you don't know based on the union of its visual and phonological components. If they were collapsed into one, you'd lose that extra information. This is just like how in hanzi there's often a phonetic component as well as a semantic component, and this does carry over somewhat to kanji even though the pronunciation is adapted to Japanese phonology.
These are all reasons why English spelling reform has never caught on, and likely will never do so. It's too widespread, and there are simply too many factors to take into account. Every language has its idiosyncracies, and to see them as flaws or try to fight them is sheer folly.
Old English
The Old English spellings for the number nine were nigon or nigen or nigan (see Dutch negen) - actually written "niᵹ[oea]n" with the old Irish "g".
For instance in "The coronation of Edgar [the peaceful]" (a poem from the Anglo Saxon chronicles, composed at the end of the... 9th century) one can read:
OE: Ond him Eadmundes eafora hæfde nigon ond XX
PDE: And Edmund's offspring had 9 and 20 [years]
Derived from nigon, you would find typically
- nigonhund ==> nine hundred :
- nigontig ==> ninety
and...
It is probably fair to assume that the "-gon" part was unstressed and this explains why there are at least three variants nigon, nigen and nigan. The vowel of the second syllable was not pronounced distinctly and gradually faded away.
Middle English
Actually the Middle English spelling shows that it disappeared pretty quickly. Here are a few spellings from Middle English.
1225 Ancr. R. 328
Þe nieðe reisun is þis.
The ninth reason is this.
c 1357 Lay Folks Catech. 232
The neynd is, that we noght yerne our neghtebur house.
The ninth [commandment] is that we not covet our neighbour's house
In nine you need the final "e" to suggest a pronunciation of /naɪn/ as opposed to /nin/ (nin).
Just as in wine /waɪn/ vs win /win/.
So that the final "e" could not disappear.
Modern English
As for ninth, however, it looks like the spellings nineth and ninth competed for a while and that ninth eventually prevailed. I don't think there's any rhyme in /-inθ/ in English that would justify the expense of an extra "e", the role of which would be to avoid the confusion between nineth /nainθ/ and ninth /ninθ/.
Here is an example of nineth in Modern English.
1688 R. Holme Armoury iii. 190/1
The Knights of St. Stephen instituted in honor of Pope Stephen the nineth.
Also note: The same thing happened to transform eahtoþa into eighth: the unstressed "o" gradually became less heard and the spelling adapted.
Sources: OED and Oxford Dictionary of English Etymology 1992.
Best Answer
There is no rule that related segments of words have to be spelled with the same sequence of letters. It might seem more logical to you, but that's never been a successful argument in changing English spelling*. We also write "deception", "deceive" and "deceit", and "reception","receive", and "receipt".
In any case, the second digraph "ai" in "maintain" is not even etymological, but secondary: according to the OED, the French source word was spelled variously as "meintenir," "maintenir" and "maynteigner." The OED entry on "maintain" further states:
So the verb "maintain" either had or developed a diphthong in the stressed second syllable when it was imported into English, but the use of the specific digraph "ai" to spell this sound was arbitrary: it could just as well have been spelled "maintein", or even "maintean" with the sound of the "ea" in "great". In Middle English or Early Modern English, before our spelling became standardized, you might encounter spellings like "mainteyne" and "deceave". The standardized spellings these words ended up with are fairly arbitrary.
The second syllable of 'maintenance" is unstressed and does not have a diphthong, so it didn't need to be respelled with "ai." Despite this, though, forms like "maintaynence," "maneteinance," "manteanance" and and even "manteignance" were sometimes used in the past according to the OED, but they did not win out in the end. I don't know if these spelling variants correspond to variant pronunciations, or if they were just affected by the spelling of the related verb as with the modern non-standard variant "maintainance."
The word "maintained" is not just related; it's actually the past tense form of the verb "maintain", so it's to be expected that we use the same spelling. "Maintain" is a regular verb in English. The words "maintainer," "maintainable," and "maintainability" all relate to the verb via common suffixes that generally take the verb as the stem without altering it (we can compare "explain," "explanation," and "explainable").
*With the marginal exception of Noah Webster, but even he didn't get all that he wanted