My current ideas:

Change the system on the main mod to allow courtiers to choose to train, separate from whether or not their employer is forcing them, even if they lack the Athletic trait.

Diligent should improve odds of choosing to train. Lazy decreases odds of choosing to train.

Sadistic should increase odds of forcing courtiers to train, and of courtiers being injured. Callous is the same as sadistic but to a lesser extent. Compassionate should decrease odds of forcing courtiers to train, and of them getting injured.

Being of a culture that values strength should improve odds of choosing to train.

If a ruler is just or humble and isn't themselves training, they are less likely to make others train. Arrogant and arbitrary rulers who aren't training are more likely to make others train.

Being of a religion that values violence should improve odds of choosing to train and making others train, especially for zealots and priests. Warmongers, and religions that have their priests set to Clerical Recruitment. Pacifists, on the other hand, have the opposite. Increased if has Warrior Monks tradition.

Women more likely to train in religions with the Sacred Childbirth tenet, especially if the physician sucks at their job. Deliberately getting strong so higher health increases likelihood of smooth birth.

Characters who are vengeful and have a rival they could duel (so limited to cultures that have dueling), at the same time as their other traits being violence-suiting (wrathful, brave, berserker, etc. Not the "poison your drink" types) will want to get stronger to try and duel that rival. Won't bother if already much stronger than that rival, unless craven, and craven characters won't try at all until they have a great advantage.

Those banned from fighting don't train, UNLESS their personalities suit them disregarding rules. Brave, wrathful, stubborn.
Being of a culture that only allows one sex to fight should make members of that sex more likely to train than they would be to if they were in a culture that allowed both sexes to fight, as there's a gender-specific pressure to be a good fighter.
Being of a culture where it's usually only the case that members of one sex can fight but exceptions are made (Right to Prove, for example), increases odds of members of that sex training, especially if they want to be on the battlefield (ambitious, brave sadist, etc).

Brave sadists and flagellants are more likely to train if they can become champions but currently aren't (they want to kill people, or get stabbed). Champions in general will be more likely to train. Craven who aren't champions less likely to train, but very likely to if they are champions (being stronger = less likely to get killed on battlefield).

Lustful more likely to train if they have no lovers (want to be more attractive. Not combat related to applies to both sexes regardless of culture rules).

Fickle characters more likely to start training, but also high odds of randomly stopping.

Greedy characters in cultures with Battlefield Looters more likely to train, and will gain money from battles.

90+ opinion of employer = more likely to train as they wish to serve that employer better. Especially if they have no other friends etc, or are in a culture with Recognition of Talent. Especially if lacking in stewardship, learning, intrigue or diplomacy.

Rulers more likely to train or make courtiers train if feeling afraid of other rulers with stronger militaries. (actually unsure how I'd code this one... yes I know how to code all the others, except the vengeful one)

Mercenaries and their champions/potential champions very likely to train. Same for holy orders. Maybe even just make them always train.

"Only the Strong" tradition: Don't bother training if 1 or 0 prowess. +10 total prowess from the strength traits won't be enough to make them a knight. If craven with less than 12 prowess, absolutely do not train as guaranteed way to avoid battlefields.

Courtiers may refuse to train even when their boss tells them to. Maybe even tiered traits depending on how heavy-handed boss is being with making their courtiers train, aka "encouraging, ordering, demanding". Each one has higher prestige cost and makes courtiers dislike you more ("has to force own courtiers to train rather than having strong knights lined up already" + "forcing me to train"). The more resistance a courtier has to training the more heavy-handed you need to be to make them train.

Right now there's no reason to take the laze around decision. If it were to relieve a significant amount of stress it might be more worthwhile. For AI they could take the decision if their over 250 stress or something like that.

AI are dragged around by on_actions rather than using decisions, or at least are in my mods because it's better for ensuring they do the things they're meant to do and has a smaller impact on performance/lag.
Added some stress impacts to the decisions themselves, and increased the stress, prestige and courtier opinion hits from forcing courtiers to train.
The reason not to train yourself is the yearly stress hit and injury risk (you can kill yourself if you train while elderly, ill or already injured), and you stop training yourself by lazing around. I might add further debuffs to training, for example the trait could reduce your stewardship or other stats, maybe the speed at which you learn your lifestyle, because time that you'd be doing your duties as a ruler or free time you'd otherwise spend learning is instead being spent on training your body.

(AI are mostly exempt from risk of killing themselves. They automatically don't train if training could get them killed. Players, however, gotta pay a little more attention)