Played a decent amount of 13th age back when it came out.
Here is what we found that it needed:
More detailed ritual casting rules, and a catalog of 4e style rituals, that include mundane things as well as more exotic rituals (e.g. create food and water, detect magic, water breathing, etc.). There should be martial "rituals" too. Basically the game needed a way to flesh out the feeling of the world, and provide more utility and non-combat abilities. The class abilities were cool, but too structured around combat scenes. The game has a wing it mentality but this is one area where more explicit mechanical framework along with a catalog of say 50 sample rituals would have been good.
Icon rules didn't work. They should be more of a narrative luck point style system. Each player rolls for each icon relationship they have. For every 6 they roll, per session they get something similar to 5e advantage, or a Savage World bennie if they can work it into the narrative of a scene, including combat scenes. That's basically what we did.
Magic items were too limited and not epic enough at higher levels. Most of them had a single power with a recharge. I'd rather have magic items with one or two always-on passive abilities, and then maybe a big bang daily or encounter power.
Also while I appreciated the unique feel of them, they were almost too unqiue and quirky. I would keep those items, but I'd also prefer a Diablo style random magical item generator so you could randomly create more standard items, and then sprinkle in some of the more specialized items.
Also class abilities were too limited. I liked the 1 Feat per level, but I hated having to waste higher level feat slots taking more feats in the chain. The Champion and Epic tier abilities of the Feat should just come automatically for free as soon as you hit that tier. So every time you get a feat it should be buying you into a whole new feat chain that just grows automatically. Sounds like this may be closer to the new approach.
Also the Paladin class was boring. I know it was intended to be a "simple" tank class, but it was boring. Needed something more. Thankfully, the 13th Age Glorantha book had that undead slaying class that could be reskinned as an awesome striker paladin, but not so many people saw that book. That class should move into the new core rulebook.
Also, there was a really good conversion of Tome of Battle done by Martin Killman on one of the fan sites. I know some people didn't like Tome of Battle, but my group loved it and we added those classes to our 13th age game to much excitement. I would love to see some version of those added to the new core rulebook. Also, add an anime style monster tamer/summoner class would be fun too. I know people cry about the action economy being broken, but those kinds of classes are still fun, and if any system can make them work it would be 13th Age.