My question is pretty straightforward : is the table core_url_rewrite deprecated or not in Magento EE 1.13+?
From one perspective (indexing) it seems so, because if you empty it, it doesn't get populated when running a full reindex. Also, after that, standard theme (RWD) does not seem to be broken.
But on the other side, once it's empty, you get nasty/system URL on some places when calling Mage_Catalog_Model_Product->getProductUrl() which turns out to still be using Mage_Url_Model_Rewrite and so core_url_rewrite.
Does it look like a bug?
My mistake, it was caused by a buggy code from a third-party module.
And to answer, yes core_url_rewrite seems to be totally deprecated after EE 1.13 can be truncated safely.