Nope, that would be the opposite. Remember this repeal is a law, passed by Congress using their authority, to affect changes in health care. So if they state up front they believe health care is a power reserved solely to the States, they've just said they don't have the power to enact any law on health care. At all.
That's a little simplistic, I'm sure if somebody had a couple of clerks and a hundred pages or so of legalese you could make a different argument revolving around the constitutionality of one specific action and not another concerning health care. And that may be what a lot of these statements come down to, a bunch of legalese and splitting hairs. Eventually codified into law and able to be challenged, BTW. But that doesn't solve their political problem, it just makes them look like they're spitting out a hundred pages of legalese and splitting hairs to do what they want to do to get around all that "plain language" of the constitution - even if they turn out to be right.
The first thing I said when I heard about the rule is it was going to bite them in the ass. This is just one of many problems they'll run into.
They do not have to cite the reasons for the law they are repealing, just the law they are writing. I do agree this rule will come back to bite them though, especially when they try to fund something that is not clearly constitutional. I still think it is a good idea, but I like the idea of a government that has problems making up new laws at the drop of a hat.
But that's the problem, isn't it? The law they are writing covers the exact same territory as the law they are repealing. If it didn't, it wouldn't be effective to do what they want to do. So if they can't legislate on that topic, they can't legislate on that topic.
What you're proposing is that Congress sit in judgment on itself and actively argue against its own authority to legislate...as authority to legislate. Let me repeat that: Sit in JUDGEment. Which is precisely why it doesn't work.
So they didn't make the argument, but then the failure to abide by their own rule draws attention to it. As a partisan talking point "Oh look, they're hypocrites", it's a little petty and not such a big deal. But when you look deeper at the fact that they just enacted the rule knowing this bill was already in pocket and claiming it's a 10th Amendment issue Congress never had the authority to address but now, conveniently, want to address it without citing authority.....rock, hard place.