Reproduction

1. place/find a block that has a loot table attached
example command:

/setblock ~1 ~ ~ minecraft:chest[facing=north,type=single,waterlogged=false]{LootTable:"minecraft:chests/underwater_ruin_small",LootTableSeed:1254937183670699988L}

2. run get command

/data get block ~1 ~ ~

3. observe that block has LootTable tag, that we want to remove

4. run command to remove LootTable from block

/data remove block ~1 ~ ~ LootTable

5. see that output says the block was modified

6. run get command again to see the changes
7. see that LootTable is still present!

Code Analysis + Potential fix

mojmap, 1.21.4

In

net.minecraft.world.RandomizableContainer#tryLoadLootTable

// after data modify/remove alters the tag, it is reloaded by the block entity
default boolean tryLoadLootTable(CompoundTag tag) {
    // since the new tag removed it, this is false
    if (tag.contains("LootTable", 8)) {
        ...
    } else {
        // causing the handler to return without updating
        // the block entities internal state of the loot table

        // the below is an example fix
        // setLootTable(null);

        return false;
    }
}