It has always been my understanding that in classic Street Fighter (ie. no focus attacks or extensive damage-scaling) and similar games that cross-up jump-ins (in addition to potentially forcing a defending opponent to guess which direction to block) usually enable an extra hit in combos for more damage.
Example: In Capcom vs SNK 2, Ryu can combo from cross-up j. forward kick into close or crouching fierce and be close enough to finish with a Shoryuken. He'd be too far to do this from a normal jump-in.
In spite of this, I have yet to see a match in which a stunned opponent eats up a cross-up combo. Are there any significant obstacles discouraging it? Is the timing any more strict to cross-up "deep" enough to reliably combo into the next attack on standing opponents (that are stunned), or is it just me?
If I just need more practice, are there any highly-regarded (particularly Ryu) players known to use this tactic? If so, what footage is available of them doing this? Do high-level players choose to forsake the additional damage of a cross-up combo to avoid error in high-pressure situations?