Your third paragraph confuses me though, because stat totals are exactly what is wrong with these races. Mythologicals get between 200 and 300 stat points IIRC, some predators get over 50, some pets more like 5. Squirrels get a laughable ONE SINGLE stat point!
Enemies do need to get stronger over time, but that is what gear and levels are for. Increasing stats via races (without level scaling a homogenised budget) will lead to either railroading of player identity as every non-Yokai/dragon form becomes worthless or massive race bloat as every one of them gets mythological variants with higher stat tiers.
And currently the stat-strong races get good unique moves too. Or at least good for NPCs, alternate-loss immob is uncounterable but too slow to be worth using as the player.
How early races like dogs or domestic cats were balanced is unknown to me. They were implemented before my time. And yes, they all suffered from power creep. The new races that I added were scaled initially more conservatively, dragons had 80 or something like that, small mammals had 30 or 40, large predators matched hyenas, which served as the framework template, at ~50. There was some further discussion about lore congruence and whether or not races should be cosmetic only, and then I re-scaled everyone of my non-mythicals to ~50, and that has been the total ever since.
As far as mythicals go, they were scaled around alicorns and demons, and for that reason basically no dragons spawn right now much to the chagrin of many. Their breath weapon intentionally maxes out at less than what a level 50 player can do with Fireball, iirc with no specialization in fire spells. Eventually, dragon TF items will be locked behind several quests, similar to how becoming a demon is no longer so easy.
This comes down to how much a race should play into player builds, and I have not gotten much direction on that. It's also been more difficult to differentiate the races ever since miss chance was removed in the combat rework, basically turning "agile" races back towards conventional physique.
I personally gave up on trying to balance the gear I made with anything except an arbitrary linear progression as using player feedback is an honor system assuming no cheat guns, with enchantment caps on, no crazy mods, etc, and it's the same story with races. Hopefully once the 2D table is complete I can arrive at a more systematic conclusion regarding tier compression, or at least some numbers to fiddle with rather than gut feeling.