Spell check (and its sibling, grammar check) have the goal of bringing something that already exists but is not conforming to a shared standard (the spelling of a word, comma usage, etc...). I'm sure an argument could be made for variances in dialect and such, but I also think most people would agree that language works better when we are using the same rules.
A fair amount of the AI is creating things that do not exist yet. That includes links between ideas. Could you write some thoughts on The Tell-Tale Heart by Poe? Probably, if you've read it or are familiar with it. Could an AI write it for you even if you've never heard of it before now? Even if you only let it finish your sentences, you could probably get something mostly correct. And if you did know about it, an AI could point you to links you wouldn't have considered.
If you're being primarily tested on spelling, then spell check is cheating. Otherwise, it's just an automated way to do a bit of professional clean-up. I can't think of a way that using something to create or link ideas isn't cheating in at least a school setting.
Also, to reply to the final line: it does matter if I can tell what you added that was made by AI and what wasn't, at least to me. I don't follow blogs to get a mindless mash-up of aggregate ideas. I follow blogs like yours because I want to know what the human thinks. If I wanted an AI's opinions on a topic, I'd generate it myself.
You could make an argument that you're still curating what's posted by rejecting what you don't like. Fair enough - that's the same as a link blog. But link blogs clearly indicate that the content isn't created by the curator of the link blog but by someone else.
I apologize if this has come off as rude. I don't mean to be. But I cannot express strongly enough how bad I think it would be for untagged AI-generated content to become the norm. I don't want the "dead internet" theory to come true.