Praying istikhaarah is not contrary to be using one’s intellect and examining matters to see which of two choices is better
Question

                What matters can one seek guidance from Istikhara and what matters are best dealt with the use of the intellect and not Istikhara?.
Praise be to Allah.
    It is not correct to divide matters, when deciding whether it 
    is permissible to pray istikhaarah regarding them, into the two categories 
    of matters which are subject to rational thinking, in which one should not 
    pray istikhaarah, and matters that are not subject to rational thinking, 
    concerning which one may pray istikhaarah. 

    Rather what is prescribed in all cases – both major and minor 
    – is to use one’s intellect and wisdom, and to study the options and 
    available means. If a person is hesitant about some matter or it is not 
    clear which choice is the correct choice on the basis of shar‘i evidence, if 
    it is a shar‘i matter, or the basis of rational proof or proof based on 
    experience, and so on, according to the nature of the matter in question – 
    if he is uncertain and it is not clear based on whatever evidence is 
    appropriate in that case, then he should delegate his affairs to Allah, 
    asking Him for guidance and declaring his helplessness before Him, and pray 
    istikhaarah, which is a supplication to Allah, asking Him for guidance and 
    success after examining the available options on a rational basis. 

    Istikhaarah does not cancel out rational thinking or 
    examining one’s circumstances; rather it is complementary to that. Islam 
    does not approve of overlooking appropriate measures or relying completely 
    on these measures; rather it is a balance between the two, so that the 
    Islamic character will combine being realistic and being spiritual at the 
    same time. 

    Hence we can say that istikhaarah is prescribed in all our 
    affairs – so long as they lie within the realm of permissibility – alongside 
    using intellect and studying the available means. 

    It was narrated that Jaabir ibn ‘Abd-Allah (may Allah be 
    pleased with him) said:

    The Prophet (blessings and peace of Allah be upon him) taught 
    us to pray istikhaarah concerning all our affairs as he would teach us a 
    soorah of the Qur’aan. 

    Narrated by al-Bukhaari, 6382. 

    Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

    It includes both important and insignificant matters, because 
    important matters may stem from insignificant matters.

    End quote from Fath al-Baari, 11/184 

    And Allah knows best.