Currently, clearing a stage of MoM completes a daily task and sends a key into your inventory.

The keys aren't tradable, so we can't broker them or send them to anyone. It feels like an unnecessary step to go into our inventory, use the key, and go back to Maws to proceed.

Any chance the task could send them straight into MoM for use instead?

I know one potential downside of this could be if people ended up with more than 8 keys as a result of it, but I can't imagine that would happen very often.

It's done that way for a technical reason.

Task Log has no attachment to the Maws tables, but it is built to award items. So it awards the Maws Key which then can be consumed to be added to the Maws database table.

Also, as you pointed out, it would cause for additional issues with wasted Keys.