No to both questions in the OP.
Conceptually Doomsday is solid. He's a personification of the very thing that we assume Superman to be up to the task to bring to heel: nature. He's every natural disaster and and wild animal given form and fist to fight back against the previously insurmountable Man of Tomorrow. Everything in the universe that acts as a reminder to us that we're small and don't have as much control as we think. THAT is Doomsday. You put a plan or a hand wringing mastermind to that and you're undercutting the whole thing by overestimating human sensibilities when held next to the vastness of creation. And that's a mistake because THAT is Clark's job in this conflict. He fights on the behalf of reason and personhood. He looks into the void and puts up his dukes as our representative.
There's only really two issues with Doomsday: His design is poor, and he's spoiled by the fact that he has any sort of a back story/explanation.
Issue one is subject, but...c'mon, right? However, issue two is where the main problem is. Like the Joker, YOU SHOULDN'T NEED DOOMSDAY'S BACKSTORY, and telling it takes something very vital from the "nowness" of him. Clark and the reader would love nothing more than to explain Doomsday, and maybe even give him a reason where common ground can be found. That anthropomorphizes him and allows Clark to but his brain to work in solving the issue. The more you explain a monster the less of a monster it becomes. Now what? Doomsday's just some sad super baby who never got a chance at life and is taking it out on the whole world? Oh? And he's also Kryptonian sometimes maybe?
Boy, isn't it nice how we can both explain why he's so strong and why he's so angry?
Know what would've been more scary? If we simply didn't know. Why's he so strong? Who knows. What did he want? Beats me. Are there more of him? No clue. You INSTNATLY put not just the world but Clark himself in more danger from then on-- not just because of Doomsday, but because of the idea that the universe just has something like that moving about unchecked. And you're not beholden to make good on that in the form of more Doomsdays or a planet full on him or whatever, but you've introduced true variability to Superman.
TLDR: Doomsday fine. He was just made in an era where by nature everything looked shitty and was over explained.