Using TR as an example of American Imperialism may have once been arguably sound but in the light of revealed history TR ends up being quite the anti-Imperialist.
Absent the USA taking over the holdings of the Spanish empire it is a certainty that by 1901 either Germany or Great Britain would have done so. Either happenstance would have put German or British forces the island of Cuba and in that a perfect launching point for a war with the USA.
Both Great Britain and Germany made competing offers to the USA to take over what we’d wrested from Spain. Germany’s offer was straightforward while Britain’s came along with their typical condescension...something to the effect that the USA was not prepared to properly run an empire. Both offers were refused and both Germany and Britain contemplated wars with the USA in order to force us to hand over those territories. Germany drew up detailed plans for an attack on New York City and that becamse the basis for a book called ‘1901’.
In retrospect it may well be that TR knew that Spain was vulnerable and that he took them on principally in order to prevent British or German control of Cuba. I personally consider TR’s actions to have been in the best interests of the USA.