You don’t need enhancement cores to level. You’d only need to infuse weapons as favorite gear for anything, armor doesn’t matter too much. The few free methods will work fine for those few weapons that you need for raid and such. If you’re infusing your favorite gear for every activity all the time then yes, you’ll run out. However you’re obviously not supposed to do that seeing how enhancement cores are fairly rare. Go awhile without infusing, collect some cores, then when you need that gear you go and infuse it. It’s really not that hard
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Which basically means that there's no point using them since you're going to need to grind either way to get the weapon rolls you want at a higher level. Remember, infusion was introduced to reduce the grind to use the gear we want. Cores just reintroduced that grind.