Rather than have cross class skills create a set of core skills that are considered basic and fundamental to adventuring. Kind of the skills you would get from attending Adventuring 101, 201 and 301.This would be a class of it's own, a 'foundation' class, and it's skills are fundamental skills for adventurers. As you level your other classes (or jobs) you can use skills from the foundation class as if they were cross class skills. The skills available would mimic the complete gamut of cross class skills we currently have with cross class skills of questionable benefit removed, along with any redundant skills where there are one or more skills doing more or less the same thing. If you look at the variety of skills available as cross class skills (when playing a class, not a job) you get some idea of the breadth of the skill pool you could draw from.

The Foundation class would automatically level with your other classes, automatically receiving extra XP amounting to 25% of whatever you earn as a DoW or DoH. You could also level it specifically by completing tasks at the Hall of the Novice. When it caps out at it's max level, you have access to all the foundation skills - based on the effective level of the class/job you are currently playing, plus 5 levels, meaning that a lvl 10 DRG could use any foundation skill up to level 15. Though you still have to slot them as 'cross' skills as you do now.

The other nice thing about doing this is that the foundation skills would be in a single defined place, and there would be no need to trait everything so that cross class skills don't function as well for others as they do for the original. Some foundation skills would be weaker versions of core class skills, such as a low level healing skill which would be weaker (say 50%) than the initial healing from Arcanist or Conjurer, but would scale more usefully than cure does, for those using it - although always being about half as powerful as a real heal from a healer.

An alternative to leveling this foundation 'class' would be to advance the availability of foundation skills based on your average DoW/DoM level. if you only ever unlock a single job and two classes, for example, your average will be relatively low. But as you level more classes and jobs, your average will rise, reflecting the fact that as you learn more about other classes and jobs, you gain the ability to use a wider range of abilities based on your advanced knowledge of other classes and jobs.

I really like having cross class skills, they are a way to express a bit of individuality within your chosen job. Of course for there to be flexibility in skill selection, the usefulness of the skills needs to be roughly equivalent, otherwise we fall back into the BiS meta for cross class skills.

Changing to an Adventurer foundation class for cross skilling makes sense as it allows you to add as many new jobs as you like without breaking the lore to explain why this new job has access to Gladiator skills, and without removing the flexibility we currently enjoy.