I want to make something of the fact that all three of the answers along the top of the grid start with A and all three of the answers along the bottom of the grid start with S, but I can't for the life of me see what that might be. It's not terribly surprising about the bottom answers, because it's so useful to have an S at the end of words.
So, yeah. 1A: Laid up (ABED) is meh. I like the clue, and the word is acceptable although essentially out of common usage. I'll give it a C-.
Which is sort of how I feel about the puzzle as a whole. Cute theme, although I feel I've seen it before. All four examples are strong, and my favorite is ICHIROSSUZUKI. But the constraints from the two 15-letter answers and two 13-letter answers lead to fill like ALECTO (couldn't pull that name from my memory, even with ___CTO) and ROARK. References to Ayn Rand are not pleasant, in my opinion.
Also, YLEM. Oof.
I like 9D: Something to keep track of? (TRAINSET). 26D: Coyolxauhqui worshipper (AZTEC) and 25D: Where Toussaint L'Ouverture led a revolt (HAITI) are fun trivia clues. HYDROX is impressively Scrabbly. It just doesn't shine.