Consequences of abnormal blood pressure unrelated to cardiac output?
Blood pressure, as you noted, is just a means to an end: the flow of blood through tissues. The trouble is, many of the body's regulatory systems use blood pressure (rather than flow) as an index of cardiovascular status. A key example is the baroreceptor system, which senses changes in blood pressure and tries to correct them by effects on the heart, blood vessels and kidneys.
In sepsis with decreased blood pressure, baroreceptor firing increases in an attempt to increase cardiac output $^1$. This increased demand on the heart can be counterproductive and cause the heart to fail. But this phenomenon is not unique to sepsis. There are many other conditions where a hyperdynamic circulation leads to heart failure: such as anaemia, thyrotoxicosis and thiamine deficiency $^2$.
All of these examples highlight a basic principle in pathophysiology: adaptations can sometimes turn maladaptive.
Note: The effects of sepsis on the cardiovascular system are complex and go beyond vasodilation. For more details, you could read a textbook of pathophysiology/medicine. Or go through any of the review articles on this topic, such as the one by Lelubre &amp; Vincent $^3$.

References:

Gattinoni L, Carlesso E. Supporting hemodynamics: what should we target? What treatments should we use? Crit Care [Internet]. 2013 Mar 12 [cited 2020 Aug 24]:17(Suppl 1):Article S4 [8 p.]. Available from: https://ccforum.biomedcentral.com/articles/10.1186/cc11502
Mehta PA, Dubrey SW. High output heart failure. QJM. 2009 Apr;102(4):235–41. https://doi.org/10.1093/qjmed/hcn147
Lelubre C, Vincent J. Mechanisms and treatment of organ failure in sepsis. Nat Rev Nephrol. 2018;147(7):417–27. https://doi.org/10.1038/s41581-018-0005-7