When it came to arguing with cover designers, sometimes I've been wrong and sometimes I've been right. I'd prefer to have been wrong, actually, but even very experienced ones do make mistakes and I have been proved right. Which didn't do me any good because then the cover designer got all huffy and didn't want to fix the problem. Arrgh.
Re your covers, I can see why they said that, since at the thumbnail size (on this site) your branding at the top is hard to read. It's bigger on Amazon, I believe. The top is similar in style to the title down below, so they're of a piece. That's branding. There may come a day when you'll want to redo your branding, but that's not what you're looking for today. Often, people do not listen when you give them very clear instructions.
Everybody's a critic. In the past I've shown off finished, paid for covers to my writers' group and they've told me what was wrong with them, which at that stage was too late, and I didn't ask for, anyway. I try not to do that to them.