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

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.