My question is:
If 結婚 is written as 結{けっ}婚{こん} rather than 結{け}っ婚{こん}, why do we write 持{も}って rather than 持{もっ}て?
Japanese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Japanese language. It only takes a minute to sign up.
Sign up to join this community結婚 is a Chinese loanword; 持つ is native Japanese. In chinese loanwords, sometimes final sounds like つ get contracted to っ〜, but because it's still 結{けつ}, the つ is still "part of" the reading. Often 2-kanji words are chinese in origin.
In the case of 持って, the っ is a suffix to 持つ's root, 持. 持 on its own doesn't have a つ sound in it. Same goes for 読む -> 読んで.
On the note of Japanese vs Chinese, you do actually get some words with っ for 2-character compounds that are Japanese in origin. An example is 引{ひ}っ越{こ}し, moving house. This one again has it because 引く doesn't naturally contain つ is the Kanji -- the kanji alone with its Japanese reading is ひ (though you would never say it alone).
Despite your confusion, you're actually asking two distinct questions unrelated to each other.
Because none of affixes involved in this case. Okurigana isn't for marking sound changes. It only clarifies some kind of grammatical meaningful differences caused by conjugation or derivation, or by homographic kun'yomi words, that could be obscured solely in kanji. For extensive explanation on okurigana, refer to this answer, but in this case, 結{けつ} + 婚{こん} → けっこん is but a regular pattern the kanji 結 transforms itself (in fact, it's more like 結 ket become ket-u when no connectable sound follows), nothing added and confused. It's just like we don't add any letter when 春{はる} + 雨{あめ} becomes 春雨{はるさめ}, or don't change spelling in English e.g. electric → electricity.
There are indeed some cases we do put っ in the middle of a word, for example, when gemination (an infix!) is added for emphasis like 奇怪{きかい} "bizarre" → 奇{き}っ怪{かい} "most bizarre; outrageous", or the word inherently has っ like 江戸{えど} "Edo" + っ子{こ} "-ic boy/girl" → 江戸{えど}っ子{こ} "Tokyoite (born and bred)".
In today's orthography, okurigana to verbs is started in the last syllable of the stem, unless the stem only has one or less syllable long. e.g. o.ku.r- → 送る, 送らない, 送って (okur- + -te > okut-te) etc. / si.ra.be- → 調べる, 調べない, 調べて etc. The standard has many provisos extending the okurigana, but reducing the okurigana is generally substandard except for a few exceptions.
Thus, the conjugated forms of the verb mot- is written as 持つ for mot-u and 持って for mot-te (持て is imperative mot-e).
Confusingly, there's a word 以{もっ}て "by means of; with" which shares the same etymology with 持つ, but normatively spelled without っ, because it's considered to be a full-fledged adverb/postposition by its own.
Because 結 don't have reading of け but けつ and 持て would be ambiguous if it's もって or もて.