When creating loot drop tables for blocks that require certain strength tools by default, adding a drop for a weaker tool does not allow it to drop items.

Example: Lapis Ore drops nothing when broken with a Golden or Wooden pickaxe. If you use the condition "match_tool" to set up a drop for wooden_pickaxe, this does not allow drops to be produced.

In this example using a Wooden Pickaxe on Lapis Ore should produce between 0 and 9 Lapis Lazuli. Even if the count is set to 100% using uniform counts, binomial p=1.0, or a direct count, the block will drop 0 lapis.

{
  "type": "minecraft:item",
  "conditions": [
    {
      "condition": "minecraft:match_tool",
      "predicate": {
        "item": "minecraft:wooden_pickaxe"
      }
    }
  ],
  "functions": [
    {
      "function": "minecraft:set_count",
      "count": {
        "n": 9,
        "p": 0.35,
        "type": "minecraft:binomial"
      }
    }
  ],
  "name": "minecraft:lapis_lazuli"
},

I believe the custom table should override tool requirements to break blocks. There a very few blocks that have tool requirements that are handled in code rather that the loot_tables.