Should I distribute stamps evenly between passports?

Like many other countries, Ukraine permits its citizens to have up to two passports, and I have made use of this possibility as a safeguard against passport loss. I now have one passport with a couple of EU stamps and another one with none.

Is it advisable for someone with two passports to travel with them interchangeably in order to get stamps into both?

Possible pros:
— Should I in fact lose a passport, the other one will have evidence of some travel history, hopefully allaying possible doubts of border control officers (not that they find me particularly suspicious; none of the three Schengen border guards I encountered have uttered a single word to me, including the first one who happily put the very first stamp into the passport).

Possible cons:
— Should I apply for a visa, the passport I submit won’t contain the entire evidence matching the travel history in the questionnaire.

Is travel history even a big deal to be worried about? Am I overthinking this? Past travels and intended destinations are Schengen zone countries.