The CDC gives this as the reason why not:
Aspiration before injection of vaccines or toxoids (i.e., pulling back on the syringe plunger after needle insertion but before injection) is not necessary because no large blood vessels are present at the recommended injection sites, and a process that includes aspiration might be more painful for infants.
[citing] Groswasser J, Kahn A, Bouche B, Hanquinet S, Perlmuter N, Hessel L. Needle length and injection technique for efficient intramuscular vaccine delivery in infants and children evaluated through an ultrasonographic determination of subcutaneous and muscle layer thickness. Pediatrics. 1997;100(3 Pt 1):400-403. DOI: 10.1542/peds.100.3.400
Other health authorities such as this one from Ontario seem to agree, citing more recent reviews:
Aspiration is not recommended. There are no large blood vessels near the intended deltoid injection site. Aspiration may increase the time it takes to immunize and be more painful for the client.
Regarding myocarditis a recent animal (mouse) study indeed found increased incidence of markers with deliberate i.v. injection. However, to demonstrate that the proposed solution, i.e. aspiration, would reduce the incidence in a real clinical setting would require pretty large human studies, as the incidence of this side effect seems to be around 1 in 15,000 or so. There are also some factors that are fairly hard to square with this (injection technique) hypothesis, namely that incidence seems to be higher after the 2nd dose:
while the Clinical Infectious Diseases study “supports the possibility that inadvertent injection into a blood vessel could result in undesirable reactions […] the majority of myocarditis cases are occurring in young males after the second dose, something that this hypothesis does not explain.”