My biggest issue is Kobo doesn't actually support epub, or at least the modern incarnation. Their reader software is woefully out of date and has terrible epub handling, so to get the features you expect you're back to the Calibre->reader loop you're on with kindle, only instead of converting to AZW3 or KFX you're converting to KePub, Kobo's homegrown version of epub they did instead. You can fix that by installing KOreader which DOES support the current epub format, but that again puts you in the same boat as the kindle (perhaps minus needing to jailbreak it) and the kindle has a much more robust community and support.

Kobos do support modern epubs, but for some inexplicable reason, they use their old epub2 renderer licensed from Adobe for all .epub files. You can just rename .epub files to .kepub and force Kobos to use the modern reader code. This gets you a lot better formatting. The catch is that location bookmarking becomes imprecise if you do this rather than use kepubify. It's super weird that they don't just offer the option to run kepubify locally on the device, behind the scenes.

This isn't really how it works though. It READS epub3, but only data that are valid epub2 structures is rendered. To get a subset (not even all) of epub3 formatting it needs to be built as a Kepub. You may be able to trick it with the extension, but there is some syntax difference. It really is a conversion if you want anything approaching true epub3 and even then its as mentioned a subset.