Why would they? During the time of the pinkertons strength they were paid and contracted to the very moneyd interests who controlled state and national governments

Besides that even though they may have outnumbered the very small national army of the 1880s and early 1890s each state still had a significant national guard

Thats besides the fact they would have lacked artillery,cavalry, and machine guns of any kind which were pretty integral to warfare by that point

So even if they some how seize a state or federal capital they arent going to be able to hold it and thats not even considering the mother of all strikes which would come in response crippling any support they had

Tldr:they would have little reason to and even if they tried it wouldnt end well for them one way or another