One reason for some of the quirks is the (generally) precise indication of consonants being broad or slender. This is reflected in pronunciation most obviously for d, t, and s. Broad d is like a hard [TH], slender d like [j]. Broad t is like a soft [th], slender t like [ch]. Broad s is [s], and slender s is [sh]. Spelling rules require that when consonants are broad they are flanked by broad vowels (a, o, u) and when slender by slender vowels (e, i). So there are often vowels that are there not for their own pronunciation but to indicate that the consonant has broad or slender pronunciation.
Many of the double-vowel and triple-vowel combinations (as in the name Saoirse [Seershuh or Sairshuh]) likely evolved out of the above rule.
Then there’s the softening (or aspiration or lenition) of consonants, which is indicated by an h after the consonant. (In traditional Irish, it is indicated by a dot over the consonant.) Some softened consonants are pronounced differently when they are at the start, middle, or end of a word. And if they are broad or slender. Often the lenition makes them silent.
Besides causing lenition, various declensions cause eclipsis of a consonant at the start of a word, a voicing or nasalization indicated by an eclipsing consonant in front, so that the original consonant after it is essentially silent. Examples are mb, gc, nd, ng, bhf, bp, dt. In words starting with a vowel, an h (sometimes hyphenated) is added before, but does not “eclipse”, the vowel.
Some declensions also cause an h or t to be added to the start of the word. If the word starts with an s, the added t eclipses it (eg, the street: an tsráid [un trawd].
Those are some of the reasons there often seems to be too many letters, even though there only 18 in the traditional alphabet.
PS: In 1948, Irish spelling was standardized and greatly simplified!
(in reply to a shared article by Barry Evans, on “do” and “-ing” forms betraying a Celtic influence in the formation of English)
Irish (these are all literally present-tense forms):
Scríobhim - I write
Tá mé ag scríobh - I am writing [at this moment]
Bím ag scríobh - I do be writing [these days] (present habitual tense of “be”)
Tá mé tar éis scríobh - I am after writing [just now]
Tá mé scríofa - I have written [in the past]
Tá leabhar scríofa agam - I have written a book
Tá an leabhar ar scríobh - The book has been written
Also of interest is the past habitual tense compared with the conditional mode:
Scríobhainn - I would write [in those days]
Bhínn ag scríobh - I would be writing [in those days]
Scríobhfainn - I would write [if I could]
Bheinn - I would be writing [if I could]
Note: “scríobh” is a verbal noun (gerund) and “scríofa” is a verbal adjective.