Using ~がる in the first person


I know how ~がる constructions work in reference to subjects in the third
person. However, I am a bit lost in regards to which situations necessitate
the use of ~がる with the first person.

For example this sentence is correct:

> 私がアイスクリームを食べたがると、母が食べさせてくれた。

But this sentence is wrong

> 私がアイスクリームを食べたいと、母が食べさせてくれた。

I don't know why.

Upon conducting some google searches in an attempt to find the answer to this
question, I found [a
source](http://blog.livedoor.jp/s_izuha/archives/6284569.html) saying that one
can use ~がる with the first person to narrate something that happened to them
in a detached manner. Interesting but not really relevant to this particular
distinction, I think. Or is it?

[This
paper](https://www.lang.nagoya-u.ac.jp/nichigen/menu7_folder/symposium/pdf/8/06.pdf)
also mentions the existence of the first person ~がる construction, but I'm
pretty sure it doesn't say anything helpful (but I could have overlooked
something).

Does anyone specifically know why 食べたがる MUST be used in the above sentences?

