As a MegaTen fan, I like the individual weaknesses and resistances even if the Digimon games that had it were not really optimized for this and you ended up just using your stronger move like Muur said instead of having to study the enemy to plan a strategy. Ideally, when you see the enemy digimon, you'd have to study its design and what you know about its lore and try an attack that you think could work and see if that pays or not, making it way more intuitive than "this plump ice dude is weak to grass because ????". I would really love an even more SMT-like Digimon game with individual weaknesses and resistences and focus on exploiting weaknesses, using buffs and debuffs and heavy resource management.
Another cool idea for a battle system is something like
[C]'s flation attacks that devaluated the enemy assets by injecting them with more money, making them more vulnerable to direct attacks - this combined with an elemental system in a Digimon game would function very well as exploiting the enemy's weaknesses would also count as a debuff and getting the weaknesses wrong would punish you buffing the enemy.
About the elements themselves, I really think poop should be an element on its own. In a system with individual weaknesses and resistances, you could remember that an enemy did not like poop attacks in the anime or see that the enemy looks very clean and try attacking it with your great
Renzoku Unchi Nage!!!!!!!!. Gross, but really fun.
Besides individual elemental resistances and weaknesses, individual digimon could have individual resistances, weaknesses and advantages in relation to other attributes, fields and even species. Wargreymon's attacks using the Dramon Killers could do .33x more damage on DR digimon and .5x more damage on Dramon-species digimon, adding .833x to your attack. Supposing that the enemy also has a weaknesses to you attack's element, your attack
X with a base value
n plus 0.833x
n should be doubled making it 2x
X - or alternatively (but not exclusively, you could have both) debuffing your enemy's defenses or something. That sounds very rewarding.
Edit: the individual attribute/field/species resistances, weaknesses and advantages could be defined by something like Pokémon's abilities so you don't have to discover what your mon can do only by yourself. You get the WarGreymon and the game tells you it can do what it does as its ability or something like that.