Thought I may as well drop this here too. This is the stat count that Flame collected some while back, and should still be relevant currently. 
[hider=Stat Data]Penny: 67
Thalia: 60
Eliza: 58
Katelyn: 57
Amaryllis: 54
Eden: 54
Sophia: 53
Serenity: 51
Janet: 51
Lily: 50
Alicia: 49
Alex: 48
Jenna: 47
Shane: 45
Trixy: 44
Hilaria: 44
Shion: 43
Su: 43 (or 47, depends on which version of AGI is correct) 
Sakura: 43
Summer: 42
Viva: 42
Valentine: 42
Emily: 41
Reaver: 41
Anaya: 40
Celia: 39
Mariette: 37
Silhouette: 37
Annabelle: 37
Tetrad: 36
Deni: 33
Connie: 33[/hider]
[img]https://i.imgur.com/xKIFnji.png?1[/img]

Around 41 to 45 is where the plateau seems to be. Dina is at 46, Charles is at 45. There's still a relatively gradual increase over all though, with only Penny being the outlier, featuring a jump in stats of seven (which could be much higher if she had spent her coinage solely on stat-raising).

An end of season reward is worth 4 stats, while one can be expected to earn another 3-4 stats based off events alone.

Past the 50-stat mark, there are no S3 characters, outside of Eden, who exist there. Note, of course, that she used her Ruby Coin (gifted from a S2 character) to gain a third specialization. Psychic gives you 4 stats, so she broke even after accounting for the -4 in stats you get from that stuff. At base then, Eden would still have 53 in stats, indicating that you could start off with fairly high stats fairly easily.

If we ignore Eden's existence, I would be comfortable with talking to the other GMs about setting a stat cap at 50. Afterwards, perhaps at the end of every season, everyone's statcap is raised by a minimum of 4 (accounting only for the End of Season reward) or a maximum of 8 (accounting also for the coinage you'd get from other stuff). Or perhaps some number inbetween.

There are other catchup mechanisms I have in mind for newer players, such as the ability to refuse the stat cap increase for extra coinage (though that sounds easily abusable) but I'll wait on everyone else's thoughts on the subject first.