No, that's not the general trend at all, in fact, when it comes to military rank in Star Wars. Dunno where you got that idea from.
Name exceptions to the trend and I'll name you more individuals that follow this trend.
That's what a "trend" is. It's not infallable, but it is association.
If you're attempting to convince people that Star Wars leaders recruit their high ranking officials from the bottom of the barrel, you're going to need to prove it.
And it;s not up to me to prove negatives, but for you to prove popsitives., There is nothing proving that Carth is competent as an Admiral, and that's the trick.
By going against logic and reasoning, you are the one attempting to prove a positive. You use Han being considered famous in everything he does as justification, yet being a War Hero doesn't quite work?
And again, I'll remind you that Palpatine's rise to power is directly related to his power as a Sith, and this has an important mythological resonance that it is very important that you should recognise in these films. It;s not even vaguely irrelevant. By that logic, if any Sith before Palpatine had been as good as him, he would have succeeded.
You also have to recognize the temporal significance.
The Ancient Sith were known threats long before they could even hope of infiltrating the Republic.
Do you really think the Republic would simply let some person that LOOKS like a threat (Ragnos or Sadow) and allow them to manipulate the Republic into their palm? Hardly.
In the same way, would Hitler have taken over Germany if it was 1900 instead of 1930? No. The circumstancse lined up for him perfectly.
And again, even this "power as a Sith" does not indicate he would swing a glowstick better than another individual. That is where the "irrelevance" lies.
You're going to have to PROVE that Political prowess = Lightsaber/battle prowess.