I agree each species needs it's own high level area like Aquatic & Dragons do, best way I've found to get other species exp is to refresh the challenges until you get a challenge that has the species exp you need at the right level, it's still tedious but if your monster can complete it itself you can basically afk it while watching youtube.
Yeah, that's the only good way to get species exp at later levels for most species since the payout-to-effort ratio challenge mode fights seem like an oversight only balanced by the fact what bouts are available is random. But I don't think I need to say how in order to grind for something you need to either get lucky or grind for tokens to gatcha it is.