You apply a relatively narrow definition of frequentism and MLE - if we are a bit more generous and define
Frequentism: goal of optimality, unbiasedness, and controlled error rates under repeated sampling, independent of the true parameters
MLE = point estimate + confidence intervals (CIs)
then it seems pretty clear that MLE, in particular the construction of CIs around the MLE, satisfy frequentist ideals (btw., it is often not appreciated that CIs in MLE, as p-values, are defined to control the error rate under repeated sampling, and do not give the 95% probability region of the true parameter value - hence they are through and through frequentist).
Not all of these ideas were already present in Fisher's foundational 1922 paper "On the mathematical foundations of theoretical statistics", but the idea of optimality and unbiasedness is, and Neyman latter added the idea of constructing CIs with fixed error rates. Efron, 2013, "A 250-year argument: Belief, behavior, and the bootstrap", summarizes in his very readable history of the Bayesian/Frequentist debate:
The frequentist bandwagon really got rolling in the early 1900s. Ronald Fisher developed the maximum likelihood theory of optimal estimation, showing the best possible behavior for an estimate, and Jerzy Neyman did the same for confidence intervals and tests. Fisher’s and Neyman’s procedures were an almost perfect fit to the scientific needs and the computational limits of twentieth century science, casting Bayesianism into a shadow existence.