Come to ～: ～てくる vs. ～ようになる

Question

Can someone please explain the fine nuances of these two? Things such as:

• Are there conditions/restrictions of when you can use one or the other?
• What are the "approximate" time periods that each covers?
• Anything else relevant...

Here's an example I saw on a particular website.

最近Xの機能を使ってきたみたい、ね！　→　What it actually said
最近Xの機能を使うようになったみたい、ね！　→　What I thought it should have said

Answer 1

It depends on the aspectuality (or more specifically, telicity) of the predicate.

• With telic predicates like 現れる, 染まる, the event described involves a change of state. There is a change within the event before and after this point. With such predicates, various forms have the meanings such as the following:

現れている (perfect)
現れてくる (gradually 現れる towards the point of view of the first person)
現れていく (gradually 現れる apart from the point of view of the first person)
* 現れるようになる (ungrammatical)

• With atelic predicates like 使う, 走る, 食べる, the event described does not involve a change of state, and is homogeneous throughout (unless there is a direct object indicating an endpoint such as このボンベを使う, 100メートルを走る, おにぎりを一つ食べる). With such predicates, various forms have the meanings such as the following:

使っている (progressive)
使ってくる (使う on the way or before coming)
使っていく (使う on the way or before going)
使うようになる (gradually/eventually come to 使う)

There is no fixed time period for 最近. It depends on the context.

Answer 2

I think (I'm not a native speaker!) that

1. ~てきた has more than one way you can use it.

a) What you talk about is something you've not planned:

やっと春がやってきた
'Finally, spring has come.'

熊ちゃんが出てくるアニメが増えてきた。
'Anime with Teddy bears in them have increased in number.'

b) Refer to an action that carries on til the time of speaking:

宿題をしてきた。/宿題を忘れて来た。
`I've done/forgotten my homework.' (What you'd say to your teacher in class.)

2.On the other hand, ~ようになる　is what you say when the result you're referring to was planned and desired, for example:

泳げるようになった！
'(Yeah,) I can swim!' (after practicing it for a long time)

Hope this helps and hope native speaker will correct me if I said anything wrong.