In the examples below
彼は私のところに荷物を送ってきた。
彼は私のところに荷物を送って来た。荷物が私のところに送られてきた。
荷物が私のところに送られて来た。
would it be better to use the termination/set phrase てきた？ (no kanji) because this is changing the nuance of the sentence? Or should it be understood literally (arrived) and therefore we て来た (with kanji) is more natural?
TL;DR: Whichever is fine, but using くる is safer.
You seem to know the basic rule, but just to make sure, this type of verb after te-form of another verb + て/で is called a subsidiary verb, and they are generally written in hiragana.
But this rule is not very strict, and every so often you will see people use kanji for subsidiary verbs, especially in stiff and stilted writings.
However, verbs after the te-forms are not always subsidiary verbs. きた in 暖かくなってきた is definitely a subsidiary verb, while 来た in 彼は急いで来た ("He came in a hurry") is a normal verb, so it is usually written in kanji. 見た in 箱を開けて見た ("I opened the box and looked (inside it)") is used as a normal verb, while みた in 箱を開けてみた ("I tried opening the box") is used as a subsidiary verb.
So the problem is this: Is きた in 荷物を送ってきた a subsidiary verb or a normal verb? How about きた in 荷物が送られてきた?
Well, I believe these きた can safely be considered as a subsidiary verb. デジタル大辞泉 clearly defines these usages under the 補助動詞 section:
９ （補助動詞）動詞の連用形に接続助詞「て」が付いた形に付く。
(snip)
㋒ある動作をしてもとに戻る。…しに行って帰る。「買い物に行ってくる」「外国の事情をつぶさに見てこようと思っている」
㋓ある動作・状態をそのまま続けながら、こちらへ近づく。また、そのようにしてこちらへ至る。「敵が押し寄せてくる」「付き添ってくる」
So the safer choice is to use hiragana for both of your examples.
But I also feel using kanji is not so unnatural in these cases, because something is physically moving. People often use the kanji 来る even in casual situations when something is physically moving to you. I personally am inclined to use hiragana for those cases, but perhaps this is a gray-area matter and it's up to the writer's taste.
In my experience, when in the 〜て＋くる form, it is more often written as Hiragana as opposed to Kanji. However, I don't think there is any major nuance difference.
In the case when there is nothing actually physically arriving and the verb is used more metaphorically, like "わかってきた” or "頑張ってきた”, I feel like it is even more common to use Hiragana over Kanji.
Personally, I always use Hiragana with the 〜て＋くる form.
Of course, if the verb was used by itself, I think it would be more natural to use Kanji (i.e. 友達が来たよ), though you could still write it either way.
Similarly, I feel that some of the other 〜て＋[some verb] forms more commonly use the second verb in it's hiragana form. Ex: "やってみる" or "置いておく"
I think the usage of whether Kanji is used is a very subtle matter, and the author's choice of which to use can be related to the tone they want to impart, and their target audience. Using Kanji generally feels more 'formal' to me.
Basically you can use either of them. However, in professional writing, you have to write subsidiary verbs in hiragana.
In 1981, Japanese government issued a cabinet directive “公用文における漢字使用等について（昭和56年内閣閣第138号）” (About Kanji Usage in Official Documents) as a part of an orthography reform. It has examples that subsidiary verbs should be written in hiragana. Most publishers and newspaper offices follow the directive also. Moreover, I was taught the rule about subsidiary verbs in a elementary school.
The directive have legal force only with official documents from the government; so you may see some subsidiary verbs which are usually used in personal communication, e.g. [致]{いた}す and [下]{くだ}す, are still often written in kanji.
