为什么I want to have a try.要加to

to have a try 是动词不定式短语做宾语补足语。
当谓语动词是Let,see, hear 的时候，做宾语补足语的不定式就要省略to：
I saw him go into the shop.
We heard the girl sing just now.

want to do sth
want to 是固定搭配
let sb do sth
let 后要加省略to的不定式嘛

have a try 是一个动词词组，一个有关的动作的东西，而且有这个词组：want to do sth.

have是动词，前面要加to。
let sb. do sth. 是固定词组，比如let's go home

want to do
let是使役动词 后面不加to

HAVE TO DO

LET SB. DO